Pfund telescope
Encyclopedia
The Pfund telescope, originated by A. H. Pfund
, provides another method for achieving a fixed telescope focal point
in space regardless of where the telescope
line of sight is pointed. This configuration utilizes a two-axis feed flat mirror to reflect starlight into a fixed paraboloid of revolution (paraboloidal) mirror, usually with a horizontal optical axis
. The paraboloid focuses through a central hole in the feed flat to a convenient distance behind the flat. No spider vanes or Newtonian secondary fold mirrors are required in this configuration. This eliminates vane diffraction and blockage, as well as secondary mirror scattering and absorption, thus improving image brightness and contrast.
The feed flat is mounted on a two-axis azimuth/elevation
mount. The azimuth and elevation drive servos must be continuously controlled as objects move across the sky, using vector addition to calculate the mirror motion in real time. One vector (V1) is stationary and points from the center of the feed flat to the center of the fixed paraboloid mirror. The other vector (V2) points from the center of the feed flat to the object to be tracked, which of course moves across the sky in time. The surface normal
of the feed flat mirror is the 3D bisector of vectors V1 and V2, normalized to unity length. If (Nk,Nl,Nm) are the instantaneous unit vector components of the mirror surface normal, then the mirror elevation angle is arcsin(Nl), and the mirror azimuth angle is arcsin[Nk/cos(Elevation)]. The field of a Pfund telescope rotates at a nonuniform rate during tracking, precluding it from long-exposure astrophotography
unless a derotation control matrix
and optics are used to compensate field rotation.
The hole in the front face of a Pfund tracking
flat should only be large enough to pass the desired field of view
with minimum vignetting
(blocking of part of the light from the paraboloid) to minimize central obstruction. The hole through the flat must be conically shaped, opening outward toward the back of the flat with at least a 45° cone, to prevent vignetting of the image by the back of the steering flat at high mirror tilt angles. A cylindrical hole would quickly block light passing through the flat from the primary mirror as the steering flat tilt angle increases.
The front reflective face of the Pfund flat must be polished extremely flat, smooth and zone-free. The flat should ideally be flat to within about 25 nanometers peak-to-valley error. Departures from flatness, from figure error or deflection, or both, rapidly introduce unacceptable astigmatism in the image. The front face should lie precisely in the plane of the elevation rotation axis to minimize the required flat mirror aperture
. This creates the need for counterweights extending forward from the mirror cell to balance the load on the elevation servo drive.
The diameter of the Pfund flat is generally larger than the focusing paraboloid, and is a design trade between fully illuminated field of view coverage and flat cost and weight. If the Pfund is intended to provide fully illuminated field coverage at a 90°Flat angle, then the minimum flat diameter must be at least
times the paraboloid diameter. The McDonald Observatory Supernova Search Telescope (SNST) used the Pfund configuration, and its feed flat diameter was 24", while the focusing mirror was an 18" f/4.5 paraboloid. The aperture stop is the rim of the focusing paraboloid, thus the feed flat has to be slightly larger than the on-axis diameter required to maximize illumination over the desired field.
Examples of Pfund telescopes are the Infrared Spatial Interferometer Array at the University of California at Berkeley. In addition to the array's website, the instrument is described in Dr. Charles Townes' book, How The Laser Happened. The same telescope is briefly described and diagrammed on pages 136-137 in Peter Manly's book Unusual Telescopes.
Apparently unaware of Pfund's telescope design, John O. Fundingsland independently developed the same optical configuration, and published his 4" aperture prototype instrument in an August, 1992 Sky and Telescope article entitled "Easy Viewing with a Fixed Telescope".
The George B. Wren Supernova Search Telescope (SNST) at McDonald Observatory and the new Wren-Marcario Wheelchair Access Telescope (WAT) at the McDonald Observatory Visitor Center (to be operational early 2007) are both based on the Pfund configuration. WAT is unique in that it will employ two 18" f/8 mirrors arranged on a north-south line and facing each other, with the steering flat halfway between. The north 18" mirror covers the northern half-hemisphere of the sky, and the south 18" mirror covers the south sky, thus providing full sky coverage, which is not possible with a single-mirror Pfund. The 24" steering flat and viewing port assembly rotate in azimuth to either mirror. Each half-hemisphere has its own fixed image location. WAT is fully compliant with all Americans with Disabilities Act (ADA) requirements and will provide both fully and differently abled visitors to McDonald Observatory with superb and comfortable viewing. A detailed Wikipedia article on the WAT will be included as soon as the instrument is operational, expected in early 2009.
August Herman Pfund
August Herman Pfund was an American physicist and spectroscopist. He was born in Madison, Wisconsin. He discovered the hydrogen Pfund lines, where an electron jumps up from or drops down to the fifth fundamental level.Pfund also invented the Pfund telescope configuration that bears his...
, provides another method for achieving a fixed telescope focal point
Focus (optics)
In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
in space regardless of where the telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...
line of sight is pointed. This configuration utilizes a two-axis feed flat mirror to reflect starlight into a fixed paraboloid of revolution (paraboloidal) mirror, usually with a horizontal optical axis
Optical axis
An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens or microscope.The optical axis is an imaginary line that defines the path along which light propagates through the system...
. The paraboloid focuses through a central hole in the feed flat to a convenient distance behind the flat. No spider vanes or Newtonian secondary fold mirrors are required in this configuration. This eliminates vane diffraction and blockage, as well as secondary mirror scattering and absorption, thus improving image brightness and contrast.
The feed flat is mounted on a two-axis azimuth/elevation
Elevation
The elevation of a geographic location is its height above a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface ....
mount. The azimuth and elevation drive servos must be continuously controlled as objects move across the sky, using vector addition to calculate the mirror motion in real time. One vector (V1) is stationary and points from the center of the feed flat to the center of the fixed paraboloid mirror. The other vector (V2) points from the center of the feed flat to the object to be tracked, which of course moves across the sky in time. The surface normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...
of the feed flat mirror is the 3D bisector of vectors V1 and V2, normalized to unity length. If (Nk,Nl,Nm) are the instantaneous unit vector components of the mirror surface normal, then the mirror elevation angle is arcsin(Nl), and the mirror azimuth angle is arcsin[Nk/cos(Elevation)]. The field of a Pfund telescope rotates at a nonuniform rate during tracking, precluding it from long-exposure astrophotography
Astrophotography
Astrophotography is a specialized type of photography that entails recording images of astronomical objects and large areas of the night sky. The first photographs of an astronomical object were taken in the 1840s, but it was not until the late 19th century that advances in technology allowed for...
unless a derotation control matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
and optics are used to compensate field rotation.
The hole in the front face of a Pfund tracking
Tracking
Tracking can refer to:*Tracking , separating children into different classes according to their academic ability*Tracking, in computer graphics, a vital part of match moving...
flat should only be large enough to pass the desired field of view
Field of view
The field of view is the extent of the observable world that is seen at any given moment....
with minimum vignetting
Vignetting
In photography and optics, vignetting is a reduction of an image's brightness or saturation at the periphery compared to the image center. The word vignette, from the same root as vine, originally referred to a decorative border in a book. Later, the word came to be used for a photographic...
(blocking of part of the light from the paraboloid) to minimize central obstruction. The hole through the flat must be conically shaped, opening outward toward the back of the flat with at least a 45° cone, to prevent vignetting of the image by the back of the steering flat at high mirror tilt angles. A cylindrical hole would quickly block light passing through the flat from the primary mirror as the steering flat tilt angle increases.
The front reflective face of the Pfund flat must be polished extremely flat, smooth and zone-free. The flat should ideally be flat to within about 25 nanometers peak-to-valley error. Departures from flatness, from figure error or deflection, or both, rapidly introduce unacceptable astigmatism in the image. The front face should lie precisely in the plane of the elevation rotation axis to minimize the required flat mirror aperture
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...
. This creates the need for counterweights extending forward from the mirror cell to balance the load on the elevation servo drive.
The diameter of the Pfund flat is generally larger than the focusing paraboloid, and is a design trade between fully illuminated field of view coverage and flat cost and weight. If the Pfund is intended to provide fully illuminated field coverage at a 90°Flat angle, then the minimum flat diameter must be at least
times the paraboloid diameter. The McDonald Observatory Supernova Search Telescope (SNST) used the Pfund configuration, and its feed flat diameter was 24", while the focusing mirror was an 18" f/4.5 paraboloid. The aperture stop is the rim of the focusing paraboloid, thus the feed flat has to be slightly larger than the on-axis diameter required to maximize illumination over the desired field.Examples of Pfund telescopes are the Infrared Spatial Interferometer Array at the University of California at Berkeley. In addition to the array's website, the instrument is described in Dr. Charles Townes' book, How The Laser Happened. The same telescope is briefly described and diagrammed on pages 136-137 in Peter Manly's book Unusual Telescopes.
Apparently unaware of Pfund's telescope design, John O. Fundingsland independently developed the same optical configuration, and published his 4" aperture prototype instrument in an August, 1992 Sky and Telescope article entitled "Easy Viewing with a Fixed Telescope".
The George B. Wren Supernova Search Telescope (SNST) at McDonald Observatory and the new Wren-Marcario Wheelchair Access Telescope (WAT) at the McDonald Observatory Visitor Center (to be operational early 2007) are both based on the Pfund configuration. WAT is unique in that it will employ two 18" f/8 mirrors arranged on a north-south line and facing each other, with the steering flat halfway between. The north 18" mirror covers the northern half-hemisphere of the sky, and the south 18" mirror covers the south sky, thus providing full sky coverage, which is not possible with a single-mirror Pfund. The 24" steering flat and viewing port assembly rotate in azimuth to either mirror. Each half-hemisphere has its own fixed image location. WAT is fully compliant with all Americans with Disabilities Act (ADA) requirements and will provide both fully and differently abled visitors to McDonald Observatory with superb and comfortable viewing. A detailed Wikipedia article on the WAT will be included as soon as the instrument is operational, expected in early 2009.