Satellite photogrammetry has slight variations compared to photogrammetric applications associated with aerial frame cameras. This document makes reference to the SPOT and IRS-1C satellites. The SPOT satellite provides 10-meter panchromatic imagery and 20-meter multispectral imagery (four multispectral bands of information).
The SPOT satellite carries two high resolution visible (HRV) sensors, each of which is a pushbroom scanner that takes a sequence of line images while the satellite circles the Earth. The focal length of the camera optic is 1084 mm, which is very large relative to the length of the camera (78 mm). The field of view is 4.1 degrees. The satellite orbit is circular, North-South and South-North, about 830 km above the Earth, and sun-synchronous. A sun-synchronous orbit is one in which the orbital rotation is the same rate as the Earth’s rotation.
The Indian Remote Sensing (IRS-1C) satellite utilizes a pushbroom sensor consisting of three individual CCDs. The ground resolution of the imagery ranges between 5 to 6 meters. The focal length of the optic is approximately 982 mm. The pixel size of the CCD is 7 microns. The images captured from the three CCDs are processed independently or merged into one image and system corrected to account for the systematic error associated with the sensor.
Both the SPOT and IRS-1C satellites collect imagery by scanning along a line. This line is referred to as the scan line. For each line scanned within the SPOT and IRS-1C sensors, there is a unique perspective center and a unique set of rotation angles. The location of the perspective center relative to the line scanner is constant for each line (interior orientation and focal length). Since the motion of the satellite is smooth and practically linear over the length of a scene, the perspective centers of all scan lines of a scene are assumed to lie along a smooth line. The figure below illustrates the scanning technique.
Perspective Centers of SPOT Scan Lines
The satellite exposure station is defined as the perspective center in ground coordinates for the center scan line. The image captured by the satellite is called a scene. For example, a SPOT Pan 1A scene is composed of 6000 lines. For SPOT Pan 1A imagery, each of these lines consists of 6000 pixels. Each line is exposed for 1.5 milliseconds, so it takes 9 seconds to scan the entire scene. (A scene from SPOT XS 1A is composed of only 3000 lines and 3000 columns and has 20-meter pixels, while Pan has 10-meter pixels.)
The following section addresses only the 10 meter SPOT Pan scenario.
A pixel in the SPOT image records the light detected by one of the 6000 light sensitive elements in the camera. Each pixel is defined by file coordinates (column and row numbers). The physical dimension of a single, light-sensitive element is 13 ×13 microns. This is the pixel size in image coordinates. The center of the scene is the center pixel of the center scan line. It is the origin of the image coordinate system. The following figures depicts image coordinates in a satellite scene:
Image Coordinates in a Satellite Scene
A = origin of file coordinates
A-XF, A-YF = file coordinate axes
C = origin of image coordinates (center of scene)
C-x, C-y = image coordinate axes
SPOT Interior Orientation
The following figure shows the interior orientation of a satellite scene. The transformation between file coordinates and image coordinates is constant.
Interior Orientation of a SPOT Scene
For each scan line, a separate bundle of light rays is defined, where:
Pk = image point
xk = x value of image coordinates for scan line k
f = focal length of the camera
Ok = perspective center for scan line k, aligned along the orbit
PPk = principal point for scan line k
lk = light rays for scan line, bundled at perspective center Ok
SPOT Exterior Orientation
SPOT satellite geometry is stable and the sensor parameters, such as focal length, are well-known. However, the triangulation of SPOT scenes is somewhat unstable because of the narrow, almost parallel bundles of light rays.
Ephemeris data for the orbit are available in the header file of SPOT scenes. They give the satellite’s position in three-dimensional, geocentric coordinates at 60-second increments. The velocity vector and some rotational velocities relating to the attitude of the camera are given, as well as the exact time of the center scan line of the scene. The header of the data file of a SPOT scene contains ephemeris data, which provides information about the recording of the data and the satellite orbit.
Ephemeris data that can be used in satellite triangulation include:
- Position of the satellite in geocentric coordinates (with the origin at the center of the Earth) to the nearest second
- Velocity vector, which is the direction of the satellite’s travel
- Attitude changes of the camera
- Time of exposure (exact) of the center scan line of the scene
The geocentric coordinates included with the ephemeris data are converted to a local ground system for use in triangulation. The center of a satellite scene is interpolated from the header data.
Light rays in a bundle defined by the SPOT sensor are almost parallel, lessening the importance of the satellite’s position. Instead, the inclination angles (incidence angles) of the cameras on board the satellite become the critical data.
The scanner can produce a nadir view. Nadir is the point directly below the camera. SPOT has off-nadir viewing capability. Off-nadir refers to any point that is not directly beneath the satellite, but is off to an angle (that is, East or West of the nadir).
A stereo scene is achieved when two images of the same area are acquired on different days from different orbits, one taken East of the other. For this to occur, there must be significant differences in the inclination angles.
Inclination is the angle between a vertical on the ground at the center of the scene and a light ray from the exposure station. This angle defines the degree of off-nadir viewing when the scene was recorded. The cameras can be tilted in increments of a minimum of 0.6 to a maximum of 27 degrees to the East ( negative inclination) or West (positive inclination). The figure below illustrates the inclination.
Inclination of a Satellite Stereo-Scene (View from North to South)
C = center of the scene
I- = eastward inclination
I+ = westward inclination
O1,O2 = exposure stations (perspective centers of imagery)
The orientation angle of a satellite scene is the angle between a perpendicular to the center scan line and the North direction. The spatial motion of the satellite is described by the velocity vector. The real motion of the satellite above the ground is further distorted by the Earth’s rotation.
The velocity vector of a satellite is the satellite’s velocity if measured as a vector through a point on the spheroid. It provides a technique to represent the satellite’s speed as if the imaged area were flat instead of being a curved surface (see the figure below).
Velocity Vector and Orientation Angle of a Single Scene
O = orientation angle
C = center of the scene
V = velocity vector
Satellite block triangulation provides a model for calculating the spatial relationship between a satellite sensor and the ground coordinate system for each line of data. This relationship is expressed as the exterior orientation, which consists of the
- perspective center of the center scan line (that is, X, Y, and Z)
- change of perspective centers along the orbit
- three rotations of the center scan line (that is, omega, phi, and kappa)
- changes of angles along the orbit
In addition to fitting the bundle of light rays to the known points, satellite block triangulation also accounts for the motion of the satellite by determining the relationship of the perspective centers and rotation angles of the scan lines. It is assumed that the satellite travels in a smooth motion as a scene is being scanned. Therefore, once the exterior orientation of the center scan line is determined, the exterior orientation of any other scan line is calculated based on the distance of that scan line from the center, and the changes of the perspective center location and rotation angles.
Bundle adjustment for triangulating a satellite scene is similar to the bundle adjustment used for aerial images. A least squares adjustment is used to derive a set of parameters that comes the closest to fitting the control points to their known ground coordinates, and to intersecting tie points.
The resulting parameters of satellite bundle adjustment are:
- Ground coordinates of the perspective center of the center scan line
- Rotation angles for the center scan line
- Coefficients, from which the perspective center and rotation angles of all other scan lines are calculated
- Ground coordinates of all tie points
Collinearity Equations & Satellite Block Triangulation
Modified collinearity equations are used to compute the exterior orientation parameters associated with the respective scan lines in the satellite scenes. Each scan line has a unique perspective center and individual rotation angles. When the satellite moves from one scan line to the next, these parameters change. Due to the smooth motion of the satellite in orbit, the changes are small and can be modeled by low order polynomial functions.
Control for Satellite Block Triangulation
Both GCPs and tie points can be used for satellite block triangulation of a stereo scene. For triangulating a single scene, only GCPs are used. In this case, space resection techniques are used to compute the exterior orientation parameters associated with the satellite as they existed at the time of image capture. A minimum of six GCPs is necessary. Ten or more GCPs are recommended to obtain a good triangulation result.
The best locations for GCPs in the scene are shown in the figure below.
Ideal Point Distribution Over a Satellite Scene for Triangulation