Sistema existente del agua potable

In the last decade of the 20th century the fast development of electronic position sensors, in particular the Charge Coupled Device (CCD), initiated a revival of optical methods in astrometry and also satellite geodesy. The key factors, when compared with traditional photographic, or even visual methods are:

− higher sensitivity, improved accuracy, shorter observation time,

− the image information is available in digital form,

− fully automatic data flow; no time consuming coordinate measurement neces-sary, and

− availability of new star catalogs with sufficient and accurate reference stars.

As a consequence, in today’s astrometry CCD technology is nearly universally applied, e.g. for the construction of ground based star catalogs (Ashford, 2001). In geodetic astronomy many classical observation techniques have been supplanted by new tech-nology based on the use of CCD (Bretterbauer, 1997; Fosu, 1998; Gerstbach, 1999;

Hirt, 2001). In the last decade various new applications have arisen in satellite geodesy (Schildknecht, 1994; Hugentobler, 1998; Ploner, Jackson, 1999). Satellites are fast moving objects and hence generate particular problems; however, much experience and many solution concepts can be taken from astrometry and classical photographic satellite tracking. The use of CCD technology in satellite geodesy will certainly grow and deliver significant results.

The basic objective is to determine the orientation of a camera with respect to the inertial frame. The camera may be either fixed to the ground (Earth based observatory) or to a space vehicle (satellite, rocket, platform, cf. Fig. 5.11). In both cases the orientation angles declinationδ0, right ascensionα0(or hour anglet0), and the swing angleκ0 around the camera axis have to be determined (see Fig. 5.7). The process widely follows the procedure that has been developed in the photographic technique [5.1]. The main steps are depicted in Fig. 5.12.

5.2.1 Image Coordinates from CCD Observations

A digital image is composed of so called pixels (picture elements) that are arranged in the form of a matrix withr rows and c columns. The image information is represented by intensities (grey values), usually varying between 0 and 255. The position of a

Earth Satellite

orbit Earth

rotation axis

Satellite

Equator

S

N

Bodyfixed z-axis (α0, δ0)

Figure 5.11. Orientation of a satellite in space

Exposure Image extraction

(stars, satellites) Star identification Plate reduction Transformation

parameters

catalogueStar

Orientation Camera, Platform

Directions to stars, satellites, other objects Figure 5.12. Process of CCD observations

pixel within the picture is defined by two dimensional coordinates (r, c), indicating the particular row and column. These are naturally discrete values. The origin of the image coordinate system is often transferred to the center of the sensor (Fig. 5.13).

The measured coordinates are hencex, y, and correspond with the plate coordinates defined in [5.1.3]. The coordinatesx_Si,y_Siof a star or satellite image covering several pixels can be determined with sub-pixel accuracy (see later). These coordinates hence are non-discrete continuous numbers.

0 1 2

2 1

0 c

r y

x

Figure 5.13. Image coordinate system Figure 5.14. CCD camera Apogee KX2E

A CCD camera (Fig. 5.14) uses a CCD sensor instead of the photographic plate or film to store the image information. The technique was invented by 1970 in the U.S.A.

The CCD sensor makes use of the photoelectric effect in silicon to convert photons into charges. The sensor or chip consists of a certain number of lines and columns

forming an array of pixels. To give an example, the CCD-chip Kodak KAF-1602E that is often used in small astrometric cameras has 1530× 1020 pixels and measures 13.8

× 9.2 mm. The pixel size is 9µm ×9µm. The corresponding field of view depends on focal length and is in most cases far below 1^◦×1^◦. Arrays of about 1000× 1000 pixels are standard. Larger arrays are available but are still rather expensive. The market, however, is developing very fast. For detailed information on CCD technology see the literature on digital photography. Photoelectricity in astrometry is discussed in detail by Kovalevsky (1995). A good overview with respect to requirements for taking fast moving objects (satellites) is given by Schildknecht (1994).

In order to obtain image coordinates for objects of interest the images of stars and satellites have to be recognized, and the coordinates of the image centersx_i,y_i have to be determined. This is the process of image extraction. The images are consid-ered to be a group of pixels with similar properties; they differ from the background through significantly higher grey values. There exist a number of techniques of image extraction, developed in the field of digital image processing. With proper weighting centering algorithms may lead to accuracies of 0.1 to 0.2 pixels for the image centers.

Depending on the camera’s focal length this may correspond to 0.1 arcseconds or bet-ter. Significant improvements can be expected with progress in CCD technology. For details on algorithms see e.g. Schildknecht (1994); Hirt (2001).

For fast moving objects like satellites precise epoch registration is of particular im-portance. For solution concepts see e.g. Schildknecht (1994); Ploner, Jackson (1999).

5.2.2 Star Catalogs, Star Identification and Plate Reduction

In the next step star images in the digital photogram have to be identified and related to the equatorial positions given by a star catalog. Because of the small field of view and high sensitivity of CCD sensors, star catalogs with a very high number of precise star positions, down to apparent magnitudes of 15^m or fainter, are required.

Such catalogs have only recently become available, or are still under construction.

Traditional catalogs are by far insufficient. Table 5.1 gives an overview.

Table 5.1. Recent star catalogs and aptitude for CCD astrometry

catalogue stars magn. stars/✷^◦ µ σpos.[^] aptitude

HIPPARCOS 118 000 12.4 3 yes 0.01 very low

TYCHO-2 2 500 000 14.5 60 yes 0.06 high

GSC 19 000 000 15.5 460 no 0.5–1.0 low

UCAC 80 000 000 16.0 2000 yes 0.02–0.07 very high

The HIPPARCOS Catalog is the main result of the HIPPARCOS mission (see [5.3.2]), one of the most important astrometric endeavors of the last century. HIP-PARCOS delivered positions, proper motions, and parallaxes of about 118 000 stars

with an accuracy of milliarcseconds. The catalog is today the most important and most accurate realization of the Celestial Reference System (ICRS) at optical wave-lengths (Walter, Sovers, 2000). It is, however, not suited for CCD astrometry because of the low density of only 3 stars per square degree. On most CCD images for the determination of directions to satellites no HIPPARCOS star would be available.

The Tycho-2 Catalog (Hog et al., 2000) was observed together with the Hipparcos mission but with lower accuracy. It contains 2.5 million stars over the complete sky. The proper motions were determined by comparison with old ground-based observations. The star density varies between 25 stars per square degree near the galactic poles and 150 stars per square degree near the galactic equator. The average position accuracy is 0.^06, and for proper motions 0.^025/year. Tycho-2 hence will be the most appropriate catalog for CCD astrometry until the complete publication of the UCAC.

The Guide Star Catalog (GSC) was compiled for the orientation of the Hubble Space Telescope (HST). The catalog contains a large number of star positions, but no proper motions. The position accuracy is rather low; the mean epoch of the ground based observations is 1983, hence the accuracy is rapidly decreasing. GSC positions are not suited for high precision work with CCD sensors.

The U.S. Naval Observatory CCD Astrograph Catalog (UCAC) (Zacharias et al., 2000; Sinnott, 2001) is under construction with the objective to provide a catalog of highest density for both hemispheres. The catalog contains positions and proper motions of stars between magnitudes 7.5 and 16 with a mean accuracy of 0.^02 to 0.^05. The results are related to the HIPPARCOS reference frame. The observations are ground based. The USNO twin astrograph has been equipped with a CCD chip of 4096× 4096 pixels, covering about one square degree of the sky. The observations started in the southern hemisphere. A preliminary data set is already released. The observations of the northern sky will last until 2003. With about 2000 stars per square degree the UCAC will be the most appropriate catalog for the reduction of CCD images in astrometry and satellite geodesy.

For the process of star identification the approximate region of the photogram is delineated in the star catalog, and the equatorial star positionsαi,δiare converted to plane tangential coordinatesξ_i,η_iusing (5.3) and the approximate camera orientation α0, δ0. The two point ensemblesx_i, y_i andξ_i,η_i are matched against one another with a suitable algorithm using translation, rotation, and scale until highest correlation is achieved. To start with, some arbitrary points from both ensembles are set to be identical. To accelerate the process, the search algorithm can be restricted to the brightest stars of the field (e.g. Quine, 1996).

The plate reduction itself follows the procedure as described in [5.1.3]. Because of the narrow field of view the astrometric model is appropriate (Schildknecht, 1994;

Ploner, 1996; Hirt, 2001). Emphasis may be given to corrections for

− astronomical refraction,

− satellite refraction,

− dispersion, and

− aberration.

For details see [5.1.3] and Seeber (1993), Schildknecht (1994), Ploner (1996).

As a result, the orientation of the camera axis in inertial space (cf. [4.3.3.2]) and/or the directions from the camera position to space objects like satellites are obtained.

5.2.3 Applications, Results and Prospects

For CCD observation of fast moving objects like satellites two particular aspects are of importance, namely the angular velocity of the object with respect to the stars or to the camera, and the intensity of light crossing the pixels. Table 5.2 gives an idea.

Depending on the telescope and the pixel size the pixel crossing time ranges between a few and several hundred milliseconds. For details see e.g. Schildknecht (1994).

Table 5.2. Observational characteristics for fast moving objects

GEO GPS LAGEOS ERS

Altitude (km) 36 000 20 000 6 000 780

Max. motion [arcs/s] 15 30 240 2000

Magnitude [m_v] 11 8 – 14 14 < 6

Telescopes can either follow the stars or the satellites, or be held fixed. Successful observations have been performed since about 1990 with existing satellite telescopes, e.g. with the ballistic camera Zeiss BMK 75 [5.1.2] in Austria (Ploner, 1996) or with the 0.5 m SLR telescope [8.3] in Zimmerwald, Switzerland (Schildknecht, 1994). In 1996 a combined Laser Ranging and Astrometric Telescope (ZIMLAT) was established in the fundamental station at Zimmerwald (Hugentobler, 1998). The mapping scale of the latter camera is about 0.^8 / pixel.

Successful observations have been reported for a large number of geostationary satellites, as well as for GPS, LAGEOS and GFZ-1. The accuracy in orientation to GEO satellites was found to be about 0.^5, and for GPS satellites 0.^1 to 0.^2 (Ploner, Jackson, 1999). Important results are, for example (Hugentobler, 1998):

− determination of the resonant geopotential terms C22andS22from precise geo-stationary orbits,

− control of space debris in high orbits and the calibration of alternative observation techniques, and

− determination of the complete position vector to satellites of interest in geodesy.

With further developments in CCD technology, e.g. larger arrays, smaller pixel size and improved time tagging the optical determination of directions to satellites will again play a significant role in satellite geodesy.