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[87] Thaw Measurement Refractor from Allegheny Observatory.

Photograph © H.K. Barnett.

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[89] The principal effort of Project Orion was to develop a design concept for an improved ground-based astrometric telescope. The imaging stellar interferometer (ISI) design attempts to incorporate as many advantages as possible while avoiding most of the problems in various existing and suggested astrometric systems. As with a Miller long-baseline interferometer, the ISI ensures low systematic errors in relative angles because it samples light received from a given star at two widely separated points. As with a conventional telescope, the ISI compares the positions of numerous stars in a small area of the sky simultaneously, hence permitting correction of both atmospheric and instrumental parameters. As with several other telescopes built or proposed, the ISI incorporates a vacuum to improve instrumental stability and internal seeing. Unlike other interferometers, the ISI measures two relative azimuth positions. Relative zenith positions, which are subject to a large amount of continuously varying refraction, are not measured.

The ISI consists of two identical interferometers. Star positions are measured near azimuths that are 30° east or west of south (fig. 34). In operation, two tracking flats per interferometer rotate.....

[90] .....about a horizontal line to accept light from a desired zenith angle and each star is tracked vertically for approximately 5 min as it passes through the field of view. Stars first observed by the eastern interferometer are seen about 4 hr later by the western interferometer. Relative positions of stars are established by measuring relative X'' positions on one interferometer and relative X" positions on the other interferometer, such as shown schematically in figure 35 for stars 1, 2, and 3 relative to star 0. Because the tracking flats rotate about a single axis and are the only moving optical elements, the system has a high degree of optical stability.

[91] In 1870, Michelson pointed out that if two small apertures are placed in front of a telescope, the light intensity in the focal plane is a "damped oscillation," such as shown in figure 36. The point of greatest oscillation about the mean intensity defines the apparent star position. In practice, the variable density of the turbulent atmosphere acts as a variable delay line, causing the apparent star position to move about its mean position. If a star's angular size is smaller than the resolution angle of the system, the intensity pattern will be as shown in figure 36. If a star's angular size is larger than the resolution angle of the system, the modulation envelope collapses toward the dotted line.

Although several interferometers operate on the above principles, the ISI is considerably different. The optics of the ISI lie in a horizontal plane, and light from a 1° by 1° region under study is reflected into the system by two tracking flats (fig. 34). The light....

[92] .....then passes through segmented vacuum windows into the main optical system. The two primary mirrors are sections of what would be the primary of a f/2 Ritchey-Chretien telescope with a 52.2-m aperture. Thus, they have off-axis paraboloidal surfaces that are slightly over 2 m in diameter. The secondary system is a figured flat consisting of two 1.85-m aspherical mirrors rigidly mounted next to each other (fig. 34).

The light reflected by the secondaries travels to an array of 20 detectors located a short distance behind the focal plane, as shown in figure 37. Each of these detectors tracks a designated star by moving along a system of ways (fig. 38). The position of the star is accurately and continuously monitored by measuring the position of the detector x with a laser system while the position of the star relative to the detector x is measured interferometrically as outlined below. The Y position of the detector is adjusted to track the star but is not used in the data reduction. The Z position adjustment is purely for focusing. An especially attractive aspect of this arrangement is that light from every star is gathered by the primary mirrors so that mirror errors are common to a star field. Yet detection is not in the focal plane so that all details of the mirror errors can be mapped. Imaging is used just to conveniently separate light from the stars in a field of view.

Within each detector (fig. 39) is a wave-front folding interferometer followed by a series of lenses, photomultipliers, and detector arrays. The wave-front folding interferometer (described in detail later) combines half of the light from the two input beams into each of the two output beams. The lenses and gratings further divide each beam into collimated beams of white, blue, yellow, orange, and red light. These beams form an image of one primary mirror and the mirror image of the other primary mirror on the photocathode of an image tube. The accelerated electrons from the images in each color impact a 16 by 16 array of charge coupled devices (CCD). Each element of the CCD array sees only a small portion of the primaries (approximately 0.4 percent) so that details of any errors on the primaries will be known. Mixing in the optical system results in each CCD monitoring the intensity signal from some point on the position scale in figure 36. A delay line scans that pattern; each detector sees a sequence of light and dark signals. If the greatest modulation occurs at a standard position of the delay line, then the detector is....

....centered on the star and x is zero. The actual position of x for each CCD element is determined each 0.5 sec. The two output beams each give four separate color beams and each beam is detected by 256 CCD elements. We then obtain 2048 independent measures of x each 0.5 sec. These measures contain information on telescope and atmospheric aberrations. The former are mappable and highly constant and therefore removable. The latter are to be averaged out to produce relative star positions from data from each interferometer.

The light-collecting system for the ISI consists of the optical elements, their mountings, drive, controls, vacuum system, and the superstructure that houses the instrument. Accuracy factors used to develop this system concept were established to maintain its inherent precision. This section discusses these accuracy requirements in terms of proposed designs.

The ISI consists of two identical imaging interferometers, one observing stars at azimuth -30°, the other at +30°. Each interferometer consists of two arms, eastern and western, each containing identical optical components, namely, a tracking flat mirror, a vacuum window, a primary mirror, and a secondary mirror. These components are described in the following subsections.

Tracking flat mirrors- Each mirror is elliptical in shape, with a major axis of 3.5 m and a minor axis of 2.2 m. The mirrors are rotatable around an axis that is parallel to the short axis of the ellipse and along the reflecting surface of the mirror. To maintain phase differences within detector requirements, the surfaces of the eastern and western tracking flat mirrors should be parallel within an angle of 0.1 arcsec. This accuracy is important because relaxing it by a factor of 2 decreases the visibility of the interference fringes almost to zero, making accurate measurements impossible.

The rotation axis should not deviate from the corresponding reflecting surface by more than 5 µm. To avoid realigning the tilt between the eastern and western tracking mirror whenever zenith distance is changed, it would be convenient to have these rotation axes parallel to the corresponding reflecting surfaces to within 0.5 arcsec.

Measurement of the relative tilt of the tracking flat mirrors is made possible by an evacuated pipe, 15 cm in diameter, joining the adjacent sides of these mirrors. A laser tracking system is installed in this pipe halfway between the mirrors. A small portion of the side [97] surface of each tracking mirror, facing the pipe and perpendicular to the main reflecting surface, is polished flat and aluminized to facilitate the laser tests.

The deviation from a perfect plane should not exceed 1 µm (for ~ 0.5 µm) over the entire 2.2 by 3.5 m surface of the tracking mirror. Any element of the surface, 15 cm in diameter, should not deviate by more than /16 from a plane parallel to the plane best fitting the entire mirror. Otherwise, fringe visibility for an individual element of the detector which "sees" an area of tracking flat about 15 cm in size would be noticeably degraded. The surfaces of the tracking mirrors, as well as those of the other mirrors, should be aluminized in such a way as to minimize polarization effects (ref. 35).

The thickness of each tracking mirror should be at least 30 cm to prevent random changes in shape in excess of /40. All mirrors in the instrument should be made of a material with a very low coefficient of thermal expansion, such as Cer-Vit or Corning ULE titanium silicate.

Vacuum windows- Vacuum windows serve as entrance pupils for the ISI. This is essential for performance of the instrument because stress birefringence in the windows would have different effects on each star in the field of view. The birefringent effects would vary with atmospheric pressure, temperature, and time. With the vacuum windows at the pupil, this effect is identical for all stars in the field and therefore has no influence on astrometric results.

Each vacuum window is 2 m in diameter. In order to be able to use a relatively inexpensive thin window, each window is divided into 0.25- by 0.25-m-square glass segments mounted in rigid steel frames. The detectors are aligned so that none of the individual detector elements "looks" at more than one square window element. Therefore, window elements need not have identical thicknesses. Nevertheless, no two of them should differ in thickness by more than 5 µm, nor should they be tilted relative to each other by more than 0.002 red. Each element is paired with one in the other window by the detector scheme. Element pairs should be obtained from the same flat to make them alike in thickness.

The window elements should be made of glass having low stress birefringence, good resistance to climatic variations, and high transmittance. Grade-A Schott BK7 glass (or UBK 7 for better ultraviolet [98] transmittance), with birefringence not larger than 600 nm/m, seems to be most suitable. Each square should be polished flat to/8 and plane parallel to 0.2 arcsec.

Primary and secondary mirrors- Each individual detector subtends an area 12.5 by 12.5 cm on the entrance aperture of the interferometer. Increasing the linear size of this area is not practical because it would make tolerances on the relative tilt of the two tracking mirrors or two primary mirrors proportionately more strict. With this design, stars fainter than twelfth magnitude cannot be observed because the photon collection rate would be too low. Usable photon flux will be considered under the discussion on detectors.

As discussed earlier, about 20 reference stars brighter than fifteenth magnitude should be visible at any time. Thus, the region of the sky imaged by the ISI should be about 1° in diameter. This requirement, together with a practical diameter of about 2 m for the maximum primary and secondary mirrors, leads to the proposed dimensions of the ISI. The secondary mirrors must be 1.85 m in diameter in order to cover, without vignetting, an area of the sky 1° in diameter, assuming that the focal length of the primary mirrors (F₁) is 100 m. For this focal length, the longest baseline, that is, the separation of the primary mirrors, for which asphericities of primary and secondary mirrors are within the present state of the art, is about 50 m, Assuming that the diameter of the entrance aperture (vacuum window) is 2.0 m, the diameter of the primary mirrors must be 2.2 m.

The primary and secondary mirrors can be considered as portions of an imaginary, two-mirror aplanatic telescope with a single primary mirror of diameter D = 52.2 m and focal length F₁ = 100 m, that is, with f/2 focal ratio. To simplify the calculations of the shape of these surfaces, the fact that the vacuum windows are entrance apertures is neglected, and it is assumed that the primary mirrors act as stops. On this assumption, the formulas for eccentricities e₁ and e₂ of the primary and secondary mirrors of an aplanatic telescope given by Maksutov (ref. 36) and Gascoigne (ref. 37) may be used:

(53)

[99] (54)

where is the ratio of F₁ to distance s, the distance from the center of the secondary mirror to the focus of the primary, and is the ratio of s to the distance from the center of the secondary mirror to the final image formed by it on the axis. The radius of curvature at the center of the secondary mirror is

(55)

The maximum deviation of each component of this imaginary two-mirror aplanatic telescope from a best-fitting spherical surface is

(56)

Secondary mirror options-There are two principal options for secondary mirrors: (1) a secondary that is flat at the center (R₂ = ) and thus minimizes alignment problems, but is very difficult to manufacture, and (2) a concave secondary that is designed to be easy to manufacture. The first option will be assumed in later sections of this report.

1. Quasi-flat secondary mirrors: Let R₂ =, which happens when = 1. Moreover, assume that the secondaries are as close to the final image as is practical without obstructing the light beams by detectors. This minimum distance is taken as s = 3.85 m, which means that = F₁/s = 26.0. Equation (53) now gives the eccentricity of the primary mirror:

The imaginary primary mirror of diameter D = 52.2 m is thus a hyperboloid of revolution, differing only slightly from a paraboloid (for which e₁ = 1).

[100] For each of the real primary mirrors of diameter D₁ = 2.2 m, the radii of curvature are calculated at its edge, at the shortest and the greatest distance x from the axis of the interferometer. In the xz plane defined by the baseline and by the optical axis of the interferometer, the radius is

(58)

In the yz plane perpendicular to the xz plane and containing a normal to the surface at a given point, the radius is

(59)

The surface of each primary mirror fits between the spherical surfaces of radii R_X = 205.54 m and R_y = 201.54 m. The maximum distance,, between these two spherical surfaces over the surface of the primary mirror is

(60)

Thus the maximum deviation of the primary mirror from the best-fitting spherical surface equalsor 29 µm.

An individual detector sees an area about 12.5 by 12.5 cm on a primary mirror. To secure good fringe visibility in the detector, the deviation of the mirror surface over this area from a perfect hyperboloidal surface should not exceed/8. Hence, over the entire surface of the primary, such deviation should not exceed about 4. The relative tilt of the two primaries (and, similarly, of the secondaries) should not deviate from the exact value by more than 0.2 arcsec.

If the secondary mirror were correcting only the spherical aberration and coma of the primary mirror, the maximum deviation nof its surface from the sphere best fitting both secondary mirrors simultaneously would be, from equations (54) - (56), for ->1, [101]

(61)

In this case, D₂ is the joint diameter of the two secondary mirrors. If each has a diameter of 1.85 m and the edges are spaced by 0.14m, then D₂ = 3.84 m, which yields = 1.93 mm. Asphericity of this magnitude is very difficult to achieve with sufficient accuracy. Probably, it is within the state of the art if a computer-assisted optical surfacing machine is used; such machines are presently in operation at Itek Co. and at Perkin-Elmer Co.

An individual detector sees an area ~5 mm in diameter on the secondary mirror. Therefore, over that area, deviations from the correct shape should not exceed/8 to secure good fringe visibility. The maximum deviation over the entire mirror surface should not exceed about 10or the detectors would operate too far from the white fringe.

The shape of the surface of a quasi-flat secondary needed to correct for spherical aberration and coma, in xy coordinates, is described by

(62)

Here y is the distance from a point halfway between the two secondary mirrors. The surface of the secondary must be further deformed to correct for astigmatism. Using formulas given by Gascoigne (ref 37), it is found that, for the ISI with a quasi-flat secondary, the astigmatism M is 1.35 times larger than for a single-mirror telescope of diameter D = 52.2 m. The deformation x needed to correct for this astigmatism is

(63)

where y is a distance from the line through the center of each secondary, perpendicular to the line joining the centers of both secondaries. In this case, the maximum additional deformation x needed to correct for astigmatism is x_max = 0.16 mm.

2. Secondary mirrors that are easy to make: This alternative should be chosen if the previously described secondary mirrors are found to be too difficult to manufacture. We assume [102] now that e₂ = 0, which is the case when a spherical secondary is sufficient for correcting spherical aberration and coma. For this case, equation (54) gives = 13, = 1.945. This is a factor by which the image of the sky on the detectors is demagnified compared to case (1). An area of sky 1° in diameter now requires a detector area only 0.90 m in diameter, separated by 3.96 m from a point halfway between the centers of the surfaces of the secondary mirrors. These surfaces are, as before, 1.85 m in diameter.

The eccentricities of the mirror surfaces are now

The radius of curvature of the concave secondary mirror measured . in the vertical plane is, by equation (55), R₂ = 16.28 m. In the horizontal plane, the radius of curvature is somewhat different because in this direction a deformation described by equation (63) is applied to correct for astigmatism. In this case, and

(65)

Hence, by equation (63), asphericity of each secondary mirror is x_max = 0.35 mm. The asphericity is still large, but the surface of the secondary mirror is toroidal in shape, much more regular than in case (1). Inquiries at Itek Co. and at Perkin-Elmer Co. indicate that manufacturing such secondary mirrors with the required precision is well within the state of the art. Disadvantages of option (2) relative to option (1) are:

1. Greater sensitivity of secondary mirrors in option (2) to lateral shifts, which should not exceed a few,um

2. Image size on the detector is half that of case (1)

These disadvantages are not serious; therefore, option (2) remains an attractive alternative if manufacturing difficulties are excessive for option (1).

The success of the telescope depends largely on maintaining the surface shape and the rotational axis of the tracking flats regardless [103] of mirror orientation or ambient temperature. The viewing angles of ±40° from the local zenith and the primary mirror diameter of 2.2 m result in an elliptical tracking flat of 3.5 by 2.2 m. Figure 40 shows the tracking flat support system.

Tracking pat cell- The tracking flat is supported in a cell designed to minimize problems of gravity deformation, thermal expansions, nonuniform external loading, and inertia forces. The tracking flat cell defines the axial and radial locations of the mirror. It contains defining pads and a means of accurately controlling the force applied to these pads. Ninety-eight percent of the tracking flat weight is supported in the axial direction by air bags. Thus the load applied to the three defining pads is limited to about 445 N. Transducers will monitor the loads applied to the pads and will be interfaced with the air-supply system. Two air compressors will be used to ensure safe operation in the event of a pump failure. Similar pneumatic support systems (ref. 38) have been found to be extremely effective in eliminating mirror deformations while minimizing hysteresis and undesirable dynamic effects (ref. 39).

The tracking flat is supported radially within its cell by a mercury column contained in an oval tube and set in a groove in the mirror cell. The amount of mercury in the tube is adjusted until there is only a slight amount of radial motion permissible. Accurate radial positioning is then completed with adjustable defining pads.....

[104] .....mounted in the mirror cell. Transducers mounted adjacent to the defining pads monitor the radial position of the tracking flat.

Support bearings- The tracking flat and its cell, weighing about 445,000 N, are supported on oil pads nestled in a cradle (fig. 40). The oil flows outward across the sill; it is filtered and then recirculated. A fluid film of 75 µm will be accurately monitored by transducers and maintained by the pump.

Preliminary calculations indicate that the maximum slewing friction at the bearings will be about 27 N^.m, and the tracking friction will be about 0.23 N^.m. Similar support systems have been used successfully with the Hale telescope and with the 1.55-m Naval Observatory telescope at Flagstaff (ref. 40).

Drive system- The drive system was designed to obtain maximum closed-loop precision in positioning, accuracy in tracking, and smoothness in operation. The accuracy of the drive system relies primarily on the gears and not on the servosystem. For this reason, the gear train selected was the one offering maximum accuracy. Other factors of less importance, such as efficiency and reversibility, were compromised.

Figure 41 shows the proposed power drive system gearing. Slewing is performed at a maximum rate of 4°/min, and the tracking rate is 0.051°/min. The tracking flat will accelerate to attain these speeds in about 4 sec.

A 4-N ^. m computer-controlled dc torque motor provides power for the tracking flat. A tachometer generator, attached to the motor, is used to obtain feedback. A torque-limiting clutch is included in the drive train to protect the gears in the event of a seismic shock or accidental collision. To minimize backlash, an auxiliary torque motor is used to constantly load the meshes to one side. The spur gear train contains three stages of reduction, with ratios of 5:1, 5:1, 5.6:1. The final and most important stage of the reduction is accomplished with a 4-m-diameter worm gear segment which has 960 teeth. It is driven by a single start thread worm having a 12-cm pitch diameter. In the past, design and construction of worm gears has been a troublesome area of telescope design (refs. 41 and 42); however, the present design solves most prior problems.

The worm is protected from impulsive-type loading by being mounted in a carriage that slides whenever the tangential force is too high. This carriage is mounted in a slide and held in position by a....

....hydraulic actuator that controls the load transmitted by the worm teeth. The worm wheel is guided by hydrostatic bearings that guide the rim of the wheel so that the worm is maintained in constant contact. A surface-hardened worm mated with a phosphor bronze worm wheel should be used to minimize friction and wear.

Position control- Two control systems, both under computer control, are used to position the tracking flats. A hydraulic rotary actuator (fig. 42) will be used to counteract the gravitational unbalanced static torque acting on the worm gear drive. This counterbalancing reduces the power required by the dc torque motor and results in smoother, more accurate, positioning of the tracking flat. A dc torque motor drive (fig. 43) is used in two modes. First, the computer uses position control at the beginning of each tracking run to establish an initial position. The system then switches to velocity control and the angular tracking motion partially corrects for the rotation of the stellar field. The angular displacements of the two flats must remain synchronized to within 0.1 arcsec. The computer provides basic drive signals to the system and uses flat position data....

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[107] ....to compensate for various system errors. The design specifications for the two control systems are given in tables 7 and 8.

Installation and alignment- Each mirror support will be mounted on a concrete foundation resting on bedrock (fig. 44). A leveled primary baseplate of steel will be mounted permanently on the concrete. Upon the primary baseplate will be a fine vertical adjustment plate (Z plate) overlain by two plates (X and Y plates) that will permit fine adjustment in two orthogonal horizontal directions. Each mirror support will attach to the Y plate.

Optical alignment of the tracking Hat mirrors will be accomplished by a single axial alignment laser (fig. 45). A laser beam within an alignment vacuum tube will be split midway between the tracking flats into two nearly colinear beams aimed at the tracking flats. At the inner edge of each mirror, the lower half-circle of each beam will be reflected to a distancing detector midway between the mirrors. The upper half-beam will pass through a vacuum tube window with vertical reticle, then cross the reflective surface of the tracking flat...

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[110] ....mirror to a half-silvered mirror with reticle. Half of the remaining alignment beam will be reflected to a second detector or visual display midway between the mirrors. If the axial alignment of both large elliptical mirrors is colinear, the two beams and reticle images will coincide; slight misalignment will result in double images and significant misalignment will show no image. The final portion of the alignment beam passing through the half-silvered mirrors will be reflected orthogonal to the axis parallel to the reflective surface of the tracking flat mirrors. The angle this beam makes with the horizontal will indicate if the reflective surfaces of both mirrors are coplanar. If greater precision is desired, interferometric methods may be used with gratings on the vacuum window and half-silvered mirrors.

The actual angles (fig. 45) are determined by laser-distancing a horizontal side (x) and a vertical side (z) of a right triangle (fig. 46)....

[111] ( and = arctan z/x). If the angles are equal, no torque misalignment exists in the large elliptical mirror. A single distancing laser is proposed to determine x, which will vary, whereas z is a constant distance that needs to be measured accurately only periodically rather than constantly. Access to the mercury base level channel (fig 47), which extends beneath the axis of each large elliptical mirror of the double interferometer system, will permit accurate placement and continued maintenance of the axes in a horizontal plane. The mercury base level channel should be semi-isolated from short-term atmospheric pressure differences. A small, optically reflective surface will be floated on the mercury at each observation point. Optical...

[112] ....alignment of the ISI is a more difficult problem because of the asymmetric optical elements involved. A laser system that permits high accuracy (ref. 43) could be used.

Enclosure for tracking flats- The tracking mirror is enclosed in a chamber. A folding door covering the top of the chamber slides open to expose the tracking mirror during observation. The opening allows the full light beam to reach the tracking mirror at all observational positions of the mirror. In the immediate surroundings of the opening, a windbreak, as well as a streamlined embankment, would be constructed to reduce wind disturbance (see fig. 48).

During the day and throughout the time period preceding observations, the folding door would be closed and the chamber would be maintained at the temperature anticipated during night observation.

Figure 49 shows the assembly of the vacuum window, consisting of a square base frame with a circular opening and a circular mounting frame. In construction, the base frame is built in position...

...first, then the mounting frame is affixed to the opening of the base frame. The steel mounting frame has a grid system spaced at 25 cm in both directions. Fifty-two pieces of BK-7 glass of various shapes tailored to fit are mounted on the grid system. Rubber seals are used to prevent leaks The maximum deformation and flexural stress of the 3-cm-thick glass sections are estimated at 7.6 µm (0.0003 in.) and 1.870 x 10⁶ N/m² (270 psi). Approximately 9 percent of the optical area is obstructed by the grid system.

The operation of the telescope requires that the primary mirrors located adjacent to the vacuum windows be segments of a paraboloidal surface with a 52.2-m diameter and a focal length of 100 m. Because the primary mirrors remain fixed in the gravitational field and are contained within the vacuum system, supporting structures can be made sufficiently rigid to ensure dimensional stability. A cellular structure can be applied to the mirror design to reduce [114] mirror weight and the weight of its supporting structure (as shown in fig. 50).

The primary mirror is positioned axially by adjustable supports that contact positioning pads on the rear surface of the mirror. A retainer on the front face of the mirror applies a small predetermined load to the locating pads. The primary mirror is located radially by a mercury-filled tube similar to those used to support the tracking flat. If necessary, edge-support locators can be provided to ensure proper alignment.

The secondary mirrors accept light transferred by the primary mirrors and focus it on a plane where it is measured and recorded by the detectors. Because the light falling on the primary mirrors is off-axis, aberrations of astigmatism and coma will occur. The secondary mirrors correct these aberrations.

[115] To correct the aberrations, the optical surfaces of the two secondary mirrors should have a relative angular displacement of less than 6 arcsec. This implies that the rims of the mirrors should be controlled within a tolerance of 60 µm. Active control is accomplished by six piezoelectric actuators mounted on a stationary ring forward of each secondary mirror (fig. 51).

The secondary mirror cells are designed so that the mirrors float axially in air-support tubes around the mirror rim. When the actuators are retracted, the mirrors move forward against retainers on the cell. The two secondary mirrors are mounted on the same support. To minimize rheological deformations, the pair of mirrors and their inserts can be rotated 180° periodically.

[116] Detector philosophy- The essence of the suggestion by A. Michelson in 1890 was that some applications of a large telescope were simpler in interpretation if small regions around two points in the entrance pupil were the only regions allowed to contribute to an interference display. In contrast, the usual direct image is the consequence of interference between all possible point pairs in the entrance pupil. The latter display becomes complicated when the wave fronts coming from points in an object scene are distorted by the intervening atmosphere by more than I wavelength. But the distortions that are positive or negative with respect to the original wave front must have equal probability over a long time period. Therefore, an average wave front must approach the undistorted wave front in shape if the scene does not change appreciably during the averaging period.

Holography is an imaging procedure that registers the shape of a wave front for each point source in the object scene. Each point must furnish a reference wave front that interferes with the directly propagated wave front when they arrive at a detector surface. In Michelson's suggestion, the reference wave passes through the other of two small apertures m the entrance pupil. In the wave-front folding arrangement introduced in figure 39, the reference wave is again from another small aperture in the entrance pupil, but this time from a region obtained by reflecting the first region through a bisecting line through the center of the large synthesized lens. The reference region could be arbitrarily chosen elsewhere in the entrance pupil according to Michelson's suggestion.

The advantage of a wave-front folding geometry is that each possible point in the incident wave front is interfered with one and only one other point of that wave front. No information is lost by blocking off large regions of the incident wave front. The interference is displayed in an image of the entrance window. If the atmosphere were absent and me telescope optical elements were fabricated and aligned perfectly, that image would be uniformly illuminated by the light from one star, no matter how the star was [117] placed in the field of view of the telescope. That field of view is narrow, of the order of 10 arcsec, because the "eyepieces" on the moving platforms are small. Positional information in the field of view is revealed by the modulation of the ideally uniform display. If the star drifts across the field of view, the display intensity cycles from bright to dark and back to bright for an angular motion of /B for light of wavelength and separation of two points by distance B. The center of the field of view is defined by the cycle of greatest modulation, a definition independent of and /B. To avoid moving the star to the center of the field of view, that "center" is scanned across the star by a known modulation of the relative path lengths from eyepiece to detector surface. Thus, position data have been encoded into a temporal dimension.

In principle, we could form one large image of the entrance window following a wave-front folding arrangement of beamsplitter and mirrors. As in holography, we could combine the light from all stars in the detector plane. Two facts make such an approach impractical. The stars of interest vary in brightness by two orders of magnitude, so the dynamic range would be excessive. The stars more than a distance from the optical axis give interference fringes of negligible depth, where is defined by the wavelength bandpass . For Q = 15, this angle is only 10 marcsec at= 0.5 µm and B = 50 m. Thus the design requires independent detector systems and synchronous modulation within each moving eyepiece.

To understand the consequences of misalignment for position measures, consider various tilts. The tracking flats should form one plane. If the atmosphere were ignored and the only tilt error in the telescope were a relative rotation of the normals to the flats about the horizontal tracking axis x by , then the wave fronts at the exit pupil would be tilted by . The tilt causes an apparent trend in star position proportional to detector y position measured from the window centerline:

(66)

Such a linear trend drops out in the average over all detectors in the aperture, but will cause serious loss of modulation depth at every detector if the linear trend exceeds/4 in a distance d across each detector. Thus, by setting y = d, [118]

(67)

In the present design, 8d = I m, so< 0.1 arcsec. Similarly, all horizontal and vertical tilt errors of tracking flat, primary, and secondary mirrors should have a sum that does not exceed.

As might be expected from our holographic analogy, the system is insensitive to focus of the collimating lens at the entrance to each detector. Let the primary telescope have focal length F₁ and the collimating lens have focal length F₂. Suppose the focal planes are separated by distance e along the optical axis. After the collimator, a plane wave front would then be deformed by

(68)

if we consider the wave front projected onto the primary. The copied and inverted version of the wave front arising from the second arm of the interferometer has a deformation centered on a different point, generally,

The intensity distribution at the image tube depends on the path-length difference which includes the term

= W₁ - W₂ = b(r₁² - r₂² -2r₁r + 2r₂r) (70)

As before, we are concerned with how rapidly this changes in distance d, so we differentiate with respect to x and multiply by d:

(71)

Note that r₁= r₂ if the star is on the axis of the collimator. The distance that the star is off-axis in the region of appreciable output modulation is about Qfd, where f = F₁/B is the focal ratio of the system. Projected on the primary, we find that

(72)

[119] Finally, the requirement on focus (apart from light missing the detector lens) is

(73)

To keep the light paths constant inside the detector, the focus range is 3.8 mm from the edge of the field of view (1.75 m diameter) to the center.

We could continue to describe how various other wave-front perturbations become visible in the interferometer display. The specification of the optical system tolerances which follows reflects the requirement that those perturbations remain small. The essential point is that a detailed data analysis scheme will permit the measurement of important system perturbations. If the perturbations are acceptably small, they may be removed during reductions. If not, they form the basis for improving alignment.

Interfacing with the ISI -We noted earlier that the light from a star in the center of the field of view travels in a horizontal plane after reflection from the tracking flats. The light proceeds to a primary mirror and a secondary mirror before it reaches the detector plane. There the rotation of Earth requires that the tracking flats turn in elevation at a constant rate to keep the central starlight in a horizontal plane. The star images at the focal plane move at a slightly variable rate in an essentially horizontal direction when the central star moves horizontally. Star detectors move horizontally at a programmed rate to follow the stars across the field of view.

Position data are to be obtained at several colors simultaneously for each star. In principle, one color is enough because the horizontal component of the angle between two stars is independent of color if the atmosphere is horizontal. The vertical component is complicated by dispersion in the air prism over the telescope. That dispersion amounts to an angle of the order of 1 arcsec from blue to red light at moderate elevation angles. But surfaces of constant density in the atmosphere may be inclined by a few milliradians due to weather fronts. Thus the horizontal component may be disturbed at the milli-arcsecond level, and such disturbance will be revealed by comparison of the position data at several colors.

A schematic suggestion for mounting traveling microscopes on horizontal rails was shown in figure 37. The microscopes are, in[120] effect, sensitive optical tiltmeters, so the supports must be rigid and smooth. The number of detectors is set by the need for at least five reference stars that will prove suitable over a decade of research on each selected sky area. Current suspicions based on stellar radial velocities suggest that 50 to 75 percent of all stars will have companion stars with periods in the 10- to 1 00-year range. Such companions are the most dangerous for the planetary search because the path of the reference star will be only slightly curved. But those that are detected must be assigned very low weight until the orbit is well established. Thus a conservative approach is to begin with 15 to 20 stars in each star field. To enable coverage of maximum area, the detectors need the flexibility of vertical motion. We shall see that the accuracy in measuring the vertical position is not critical for the proposed detector scheme. Coarse adjustment and no further motion during observation should be possible. The detectors have finite vertical dimension so the stars must be selected on a noninterfering basis for both telescopes. When the detailed detector design is undertaken, a small excess of detectors should probably be provided to attain enough stars. One possibility is to install two detectors per rail and an optical Bat at each end of the rails shown in figure 37. A laser interferometer would be needed at each end of each rail set plus one or two more interferometers to check the distance between the two optical flats. The extra complication of aligning and monitoring a second reference surface must be considered in such a choice.

Tracking- Figure 38 is a sketch of an individual detector or unit and an associated Cartesian coordinate system. The device is mounted on four preloaded, "open-type," linear ball bearings and is free to move in X on the two outer round ways over the entire field of view ( 1.75 m). The cylinder ( 15 cm long, 9 cm outside diameter) containing the optics and imaging tube is free to move on Y ways over a distance of 9 cm centered on the central way. Small movements in Z (~3 mm) are also possible for focusing purposes. The I required motions in X, Y, and Z and a means for obtaining them are discussed below.

[121] The central way shown in figure 38 is associated with the X drive mechanism. The drive should reach a constant velocity of ~0.7 cm/sec in 0.5 sec from rest with the capability for small corrections (1 mm or smaller) during an observation. The total slop in X should be less than 10 mm. Transients should be sufficiently damped within 1-2 sec of startup; additional transients introduced by the correcting mechanism must be kept small. Capability for fast return should be included to maximize observation time.

Three possibilities for the X drive will be discussed: (1) piezoelectric drive, (2) lead screw, and (3) servo-chain drive.

Piezoelectric drive: This drive makes use of a piezoelectric "inchworm" (Burleigh Instruments, East Rochester, New York) sketched in figure 52. This device uses a sequence of electrical pulses to effect a series of mechanical deformations of the quartz crystal (as shown in the figure). At the completion of one sequence, the device has taken one step along the rod. In the present application, a slotted cylindrical device would be used to grip the third way and translate the device in X.

The current specifications for this device are given in table 9. Current technology does not include a device with sufficient speed, overall length of movements, or proper geometry for the proposed application. Slow return slewing speeds would also limit observation time. However, the inherent simplicity and accuracy of the device make its use desirable, and a segmented device of many central segments should be investigated as a means of overcoming the above deficiencies.

Lead screw: A lead screw with either a double-nut preloaded ball nut or spring-loaded Teflon rings serves as another drive alternative. Rohlix drives also provide a similar function.

Servo-driven chain: A servo-driven chain running in a groove cut in the top of the central way and attached to the detector at its mass center is a third alternative. The chain is driven by one or possibly two dc servo motors and a linear encoder permits feedback position data. The cost of this system is expected to be less than the others described above.

The Y position is fixed during an observation and is approximately known for each star expected within the field. However, some correction in the expected Y position may be necessary during.....

....the initial observations of a given night. The Y motion of the optics will be produced by the inchworm device.

The focal plane is a doubly curved surface of 100-m radius of curvature. The required Z position of the optics, needed for focusing, is a known function. The motion may be provided by a linear actuator situated behind and driving the cylinder containing the optics/ image tube along its axis. Driving the actuator by a dc motor/encoder/gear box combination will provide a 1.0-µm resolution. The cylinder would be supported on ways and would be spring-loaded to minimize backlash.

The X position of the optical head and its tilt about the Y axis must be determined with interferometric accuracy. The proposed laser system and flat reference mirror are shown in figure 38.

The flat mirror extends over the entire height of the detector region and serves as the fundamental reference relative to which measurements of X and tilt about the Y axis are made. The tilt measurements provide a small correction to X position measurements. It is necessary to know of the tilt around the Y axis because of the roughness of the ways-of the order of a few nanometers. These changes in the orientation of the optic axis of the collimator multiplied by the focal length F₂ become changes in the apparent X of the traveling microscope. The easiest of several ways to monitor this tilt is to [124] mount two cube carriers on each platform in the XZ plane and to run two laser interferometers on the platform, referring each to the reference flat.

Defector optics- The optical system within the detector is sketched schematically in figure 53 and orthographically in figure 54. The system is basically a wave-front folding interferometer in which the beams are modulated and mixed as described below.

Light from each of the primary mirrors is first passed through a chopper which is part of the star acquisition scheme discussed below. Lens L1 serves to collimate the two beams, after which they enter the Koester prism, K1, are reflected, and passed on to roof I or to the internal reflecting cube corner. Roof 1 serves as a piezoelectrically driven modulator. A phase difference of [Greek letter] pi radians exists between light entering prism K2 from the cube comer and light entering K2 from roof 1. Koester prism K2 contains a beamsplitter (mixer). The light beams now pass out of K2, still collimated, and enter roof 2, which redirects the beams. Roof 2 also has a diffraction grating in the path of the emerging beams which disperses the light. The dispersed light enters lens L2, which throws the pupil to infinity and forms an image of the star at distance F beyond L2. Here F is the optical path length from the mixer to lens L2.

Lenses L3 and L4 are at a distance 2F from L2; lenses L3 and L4 have focal lengths F/2 and F, respectively. Lenses L3 serve to image the star in the photocathode. Lenses L4 are central slabs cut from convergent lenses that serve both to define the passbands of blue, yellow, orange, and red light and to image the entrance window on the image tube photocathode. To avoid a dispersed image of that entrance window, a blazed grating identical in line spacing to the first grating is placed under lenses L4. It completes the recollimation of the beams that left the exit pupil at the beamsplitter. The image tube is at distance F from lenses L4.

Detector electromechanical functions- As outlined previously, an optical delay line is realized in one path of the detector interferometer in the form of a roof prism. It will be scanned electrically over an optical path difference of about 50 wavelengths in about 0.5 sec in a sawtooth pattern. The delay line will be moved at, say, 56 mm/sec. Unfortunately, at least for the total scan distance visualized above, the integral linearity error is apt to be ±5 percent. Repeatability can be quite good - less than 1 percent-but the.....

.....linearity in the voltage-to-displacement characteristic usually creates a problem. This can be easily corrected by storing the inverse nonlinearity in a read-only memory and performing the required transformation.

Figure 55 is a block diagram for a piezoelectric (PZT) delay line scanner. Upon receipt of a synchronizing pulse from the central data processor, the up-down counter registers another count. The stored count is transformed into a different data word by the read-only memory (ROM), thus producing the required signal for a position change, The ROM is followed by a digital-to-analog converter that provides a voltage drive for the high-voltage amplifier. The voltage amplifier produces an output voltage swing of about 1000 V for the PZT drive. The resultant voltage is read by a digital voltmeter for position confirmation. This voltage is retransformed by another ROM, in which the PZT nonlinearity is stored, and sent back to the central processing unit.

The above process is repeated for each advance pulse and, when the up-down counter reaches full count, the mode is reversed. The delay line then sweeps in the reverse direction.

Detector configuration- Since space is at a premium in the tracking detectors, a primary consideration is size. Weight is also a prime factor since each detector must track its appointed star rather rapidly. Power consumption must be low for obvious logistical reasons, These parameters, when considered jointly, underscore the attractiveness of charge coupled device (CCD) imagers. Signal-to-noise considerations imply the necessity for image intensification (ICCD operation).

As mentioned previously, each image tube will process two white-light star images. In addition, each tube will have arrays to process four passbands centered, for example, at 0.45, 0.52, 0.59, and 0.66 µm. There are two arrays for each of these colors. The two arrays have the property that corresponding CCD elements are anticorrelated in output, a property we would like to exploit.

[128] The overall configuration of the detector is depicted in figure 56. Light rays from the detector optics fall upon the photocathode, releasing photoelectrons on the other side. These electrons are accelerated toward the CCD arrays by a high voltage. When they reach the CCD arrays, they produce secondary electrons in the semiconductor substrate. This is a gain mechanism. Gains of several thousand have been reported at electron energies of about 10 keV or so (General Electric Company, internal report, 1976). Alternatively, the fast electrons impact on a phosphor on the output face of a sealed image tube and the subsequently emitted light is transported through a fiber-plate coupler to the CCD array.

[129] The sketch in figure 56 shows the arrangement of electron beams in the image tube. Each square array is a CCD imager assumed to be operating in the EBIC (electron-bombarded, induced-current) mode. An "on-chip" integrating sense amplifier will be provided for high signal/noise ratio. Information coming from the arrays emerges as discrete-time analog samples, 10 lines in parallel. Their further processing will be described subsequently.

Detector functions -As pointed out in a previous section, there is space for housekeeping functions in two compartments between the X ways. Above them is a slide that moves in the Y direction upon which the optical equipment is mounted. This section of the report outlines the electronics and logic functions that are physically distributed in the moving detector carriage shown in figure 57.

A receiver antenna is mounted on the compartment beneath the X ways. It feeds a demodulator, and the demodulator drives a demultiplexer The demultiplexer derives the following commands in the form of data bit streams: (1) a move pulse to cause the delay line to increment by one-quarter wavelength, (2) an array read clock to shift information from the CCD arrays, and (3) a data stream to actuate the focus, or Z axis, controller.

The delay-line logic is performed in the same package as the data receiver, the objective being to remove heat-generating and space-consuming components from the vicinity of the optics. The high-voltage drive to the PZT actuator will be cabled up to the slide. The array read information will also be fed directly to the slide, along with low voltage for the integrated circuit logic package on the slide and high voltage for the accelerating portion of the image tube. Low voltage will be transmitted to the moving carriage along the X ways and will be picked up by wipers. This voltage will be regulated and also transformed to higher voltage (several thousand volts dc). Because wipers sliding on metallic ways generate noise spikes, care should be exercised in voltage regulation and in the suppression of noise spikes.

The instrument package aboard the Y-slide is a multifunctional one. It accepts the high-voltage drive and actuates the PZT element. The DVM and ROM part of the delay line actuator logic resides here, along with a buffer to store the position data. These data are fed into a multiplexer along with the array outputs after analog-to-digital....

conversion. These composite data are then modulated upon an rf carrier and fed to the transmit antenna affixed to the Y-slide.

Additional electronics functions housed in this portion include the clock logic to derive all on-board control signals plus the drive for the focus, or Z-tracking, controller. An auxiliary data channel is provided for any other functions desired.

Summary of data handling- Data routing, acquisition, fringes, and traveling detector positions and tilt are summarized below.

Data routing: A schematic functional diagram of data routing on board the moving detector is illustrated in figure 58.

Acquisition: in order to acquire its appointed star, each detector must initially be placed in an acquisition mode. Because its operation has been described elsewhere, it suffices here merely to mention that the data required for acquisition are contained in the bit stream from the white-light channel arrays. Hence, these data are routed to the central processor via the multiplexed data stream.

Fringes: As the delay line changes position, the temporal fringes in each beam of colored light make the image of the superimposed input windows appear to blink, depending on the color of the light, at about 100 Hz. Varying intensity is sampled at each photosite in the CCD detector array. The bit stream emanating from the detector array represents digitized versions (8 bits/sample) of the detector photosite intensity.

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[132] Traveling detector position and tilt: A laser interferometer means is provided for ascertaining the X position and tilt of each detector. Such a scheme is illustrated in figure 59. The interferometer consists of a Koester prism, as in the detector optics. Outputs X and Y are electrical signals complementary to one another. The succeeding electronics package removes a carrier wave from X and Y, counts low-frequency fringes relative to a calibrated origin-in a bidirectional sense-and reads each zero crossing to approximately one-twentieth of a wavelength¹ (Hewlett-Packard Company, application No. 197-1, 1975). Note that the bidirectional requirement is a consequence of the occasional retrograde X motion of the detector. The laser and the signal demodulators can all be arranged to be outside the vacuum.

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[133] Data reductions for star image position -The signal seen by a CCD element in one of the eight images of the entrance window is of the form

where t is a relative path difference between the corresponding points in the two entrance windows that have been superimposed by the folding of the wave front about a line midway between the windows. The modulation depth V, which has a maximum t = t₁ corresponds to a visibility function in a Michelson wavelength spectrometer if the beamsplitter divides the energy evenly between the two arms. Otherwise, the modulation depth is proportional to the smaller fraction in a split of fractions f and 1 - f. The dc level U contains no position information, but is of interest for photoelectric photometry of the star.

In space or on the Moon, we would scan the path difference and find the star position in the field of view of the microscope from t₀ as a result of a least-squares fit of I(t) to the entire waveform. But the atmosphere moves the star position, as we saw in an earlier section, by an amount corresponding to t = 10 at frequencies up to 1 Hz. This implies that fringe speeds up to 20 [Greek letter] pi waves/sec are common. That means that if we modulate t at 100 waves/sec, there will be some moments when the star position just keeps up with the intentional motion and successive samples of I will be the same because t - t₀ is slowly changing. And there will be other moments when the apparent modulation rate is doubled or more. Clearly, we need a scheme that pays attention to a less rapidly varying quantity than t₀. Such a quantity is the modulation depth V(t -t₀). if is a measure of the width of the spectral bandpass falling on one detector, then V falls appreciably below its maximum value outside a region of t - t₀ about Q waves wide. More precisely, the modulation depth V is the Fourier transform of the effective energy distribution incident on the detector, including all instrumental effects such as wavelength-dependent quantum efficiency and so on. We cannot avoid having to sample I at least 200 times per second, which means few photons and high data rates from 256 detectors per exit pupil and 8 exit pupils. But we can hope to sum at least Q of those samples in some manner that reveals an average of V in a [134] "small" region of its variation. That will decrease the data rate by a factor of about Q.

There are several possible schemes to detect the modulation depth V. Basically, we need to detect the fluctuating part of 1, rectify, and sum. The output will include a noise component, which tends to make it difficult to locate the path difference t where V has its maximum. But, in the case of quantum noise, it can be shown that the noise is correlated with V, so it may be expected that the method will work even if there are few counts per Q samples per exit pupil array. For example, for a fifteenth-magnitude star in a 0.05-µm passband centered at 0.5 µm, there are about 500 electrons per second per aperture of, assuming 15-percent quantum efficiency and 50-percent transmission after reflection and grating losses. Combining the two images of the input window in that color, we find 50 counts per 1/20 sec. If the atmospheric phase fluctuations do not exceed nor appreciably decrease the depth of modulation, then the formal uncertainty in star position after the 300-sec integration would be /(BN^1/2) = 50 µarcsec, where N = 1.5 x 10⁵ is the total number of electron counts. But we saw earlier that the atmospheric phase fluctuations are indeed bounded by about. And if the modulation scheme is as rapid as called for in the previous paragraph, it is clear that appreciable decreases in the modulation depth will be occurring less than a third of the time. Thus we satisfy the formal requirements at the fifteenth magnitude for small to negligible uncertainty in the star position at the 100-µarcsec level due to quantum statistics.

In discussing possible schemes to detect the modulation depth V, let us first understand that all four passbands can be studied simultaneously, despite the fact that the roof speed is not ideal for any passband. Let the effective wavelengths be = 0.45, 0.52, 0.59, and 0.66 µm as listed in table 10. Suppose the roof speed is defined by a linear sweep of 14 µm in 0.5 sec. Then the rate of optical path change is 56 µm/sec, or 100/sec at the intermediate wavelength of 0.56 ,µm/sec. Then at = 0.45 µm the fringes go by 24 percent faster. Thus, if a sample No. 1 were centered at 0 phase, sample No. 3 would be at 180° for = 0.56 µm but at 224° for = 0.45 µm. Now the cosine of 224° is -0.72 instead of -1.00, so if we subtracted sample No. 3 from sample No. I and kept only the absolute value as a measure of the modulation depth, we would have an estimate that....

Wavelength
.
0.45	0.860	0.804
.52	.985	.900
.59	.994	.884
.66	.944	.815

....is 86 percent of the maximum estimate (column 2 of table 10). But the fringes are moving. If we sample the light output p times per cycle, then the blurring decreases the apparent depth of modulation by a factor of . The apparent V for this sampling scheme is column 3 of table 10. The passbands closest to 0.56 µm have the deepest modulation, but all have modulation greater than 80 percent when the star is not appreciably resolved and the fringe speed due to the atmosphere is zero. Such a sampling scheme is motivated by the fact that, if a sinusoidal wave is sampled four times per cycle, then the least-mean-square fitting procedure involves sines and cosines that are all ±1 or 0. Thus, digital multiplication can be replaced by the much more rapid addition or subtraction. Indeed, if the four samples I_j in one cycle are to be fitted to

we find, in the absence of blurring,

then if we take UV = |a| + |b|, we approximate the hypotenuse of a right triangle by the sum of its two sides. For random fringe position, [136] this overestimates UV by 4/[Greek letter]pi = 1.27 and gives a special role to the phases that are close to odd multiples of [Greek letter]pi /4 where the error in modulation depth is largest, 41 percent.

In a second possible sampling scheme, suppose that we have time after an analog-to-digital conversion of each CCD output to form P by digital multiplication. Successive values of I² for a given detector can be represented by

Ignoring the atmosphere, we see that for the passbands of table 10, the average of I² for four samples will be significantly different from U² + v² because the average of coswill be quite far from zero. However, it is easy to select a time interval about Q half-cycles long at = 0.56 ,um for which the average of cosis less than 1 percent for each of the four passbands. Since such an interval is adequately small for a measurement of the center of V, we can estimate V² from <I²> - <I>² with negligible systematic error in any passband. In fact, because of the slow drift of cosin that averaging period, the sampling frequency could be decreased from 400 to 200 Hz, which is the Nyquist frequency for = 0.56 µm. The danger of sampling a pure sinusoid at exactly the Nyquist frequency is that, instead of sampling maximum-minimum-maximum and so on, the sampling might be mean-mean-mean and so on. No such danger exists for passbands not containing = 0.56 µm and is irrelevant for a long-term average in the presence of atmospheric perturbations larger than /2.

In a third possible sampling scheme, we recall that, for corresponding detectors in the exit pupils of a given passband, the outputs are proportional to, say, and ,where R is a factor for relative sensitivity of the two detectors. Then

It is clear that if the relative sensitivity factor R were close enough to unity for every detector pair, we could use the complementary outputs for the separation of the dc level and the modulation by the [137] simple process of digital sums and differences of simultaneous outputs from corresponding detectors (which is not trivial from a programming point of view because the exit pupils are mirror images, but the CCD arrays are not apt to be read out in that order unless we require it at manufacture - a stipulation that would increase cost). Experience with diode arrays at the University of Arizona suggests that deviations of R from unity are apt to be about 5 percent. This suggests use of the positive definite statistic:

which increases with UV above a constant but small bias of U|1 - R|. Such a statistic is suitable for finding the position of the maximum value of V with minimum complexity provided each R1.

To compare the first and second sampling schemes, it is enough to show that present hardware is capable of meeting the timing requirements of the second scheme so that the shortcuts of the first scheme are not necessary. Suppose 200-Hz (Nyquist) sampling, so that there are 5 msec per cycle in a 500-msec sweep through 14 µm of roof motion. One possibility among many is that a microprocessor is provided for each 128 elements of a photoarray. With 256 detec-tors per exit pupil and 10 such arrays, this calls for 20 microproces-sors. The time allotted for each detector, then, is 39 µsec. In 39 µsec we must do an 8-bit analog-to-digital conversion, add I_J to the appropriate register (12 bits), form I_j², and add it to the appropriate register (20 bits). That time needs to be allocated so that after 10 cycles the results in the summing registers can be shifted out to buffers for transmission to a general purpose minicomputer. The transmission rate is then, ignoring imaging array used for acquisition, l 6 arrays by 128 detectors by 32 bits/50 msec = 1.31 M bits/sec for each detector. A digital multiplier capable of forming a 16-bit product in 13 µsec is manufactured by American Micro Devices, among others. An 8-bit analog-to-digital conversion in 13 µsec is reasonable, so that leaves 13 µsec for two additions, some counterincrements, and logic checks. If this 39 µsec were somehow not adequate, we could double the number of microprocessors unless heat dissipation and volume prohibited.

[138] In the above example, the next processing task would be to calculate the total variancefor each detector. There would be some advantage of calculating it before transmission because it is not apt to be more than a 12-bit number. Total variance and could also be averaged with the corresponding detector in the conjugate exit pupil and further decrease the bit rate by 1/2. Then the set of numbers S(t - t₀) for each detector can be combined for an estimate of t₀; the example has 10 numbers per sweep for four colors and 256 detectors per color, requiring only 10,240 numbers in core. It seems probable that the fastest way to obtain an estimate of t₀ involves a fast Fourier transform of S, because the lowest Fourier component could be slightly corrected in phase for instrumental effects in the optics before averaging all the detectors in an exit pupil. The correction in phase would require only four multiplications per detector after looking up at most 2048 numbers in a file. The phase corrections should markedly decrease blurring of the t₀ distribution. After averaging the t₀ values over the exit pupil, we are left with four values of t₀ and , one for each color. For photometry we would also like to record the average over the pupil of , where correction is included for relative sensitivities of the detectors, if needed. The large data rates per star suggest that each transmitter be followed by an arithmetic and memory unit per star that is slaved to the central processor. Data rates are low when t₀ becomes available. The t₀ values are to be monitored by the central processor to ensure that each traveling microscope follows its star successfully.

Long-term stability is essential for both the site and its supporting structure. To achieve this stability, it will be necessary to obtain a firm bedrock site condition along with a massive and continuous reinforced concrete foundation.

Many alternative schemes are possible and the following basic structure is given to provide at least one workable method for feasibility and cost analyses. There are three basic types of foundation elements:

1. Heavy reflector footings; 1 m thick and heavily reinforced to ensure stability

2. Vacuum tube footings; 0.5 m thick, moderate reinforcement

3. Intermediate working area slabs, 0.3 m thick, moderate reinforcement

After the foundation is completed and the walls are poured, the vacuum tubes and utility services are placed, the support structures for the heavy mirrors and reflectors are installed, and finally the optics are placed. The precast roof slabs are then installed, followed by waterproofing and insulation, for example, a 1-ft thickness of pumice material. Final earth embankment, grading, and landscaping should then be completed.

The surrounding site grounds should also be covered with 0.15 - 0.30 m (6 - 12 in.) of pumice or other suitable, vesicular rock to insulate the entire installation and to provide the least absorption contrast with the surrounding environment.

To minimize refraction changes and resulting distortion along the horizontal light path, it is necessary to enclose this path in a vacuum. The proposed design encloses the primary mirrors, secondary mirrors, and detectors in an evacuated tube, leaving the tracking flat mirrors outside the vacuum system. The entire vacuum system will be evacuated to a pressure of 1 Torr (1 mm Hg) which is relatively easy to reach with existing equipment. The temperature and vacuum systems must be able to keep the vertical temperature variation within the tube to less than 1°C.

For any astronomical observatory to be successful, an optically sound telescope must be located at a site that minimizes the negative effects of atmosphere and weather on individual observations as well as on the observation program.

High percentage of nighttime clear weather -To maximize the number of astrometric observations, the nighttime sky at the site should be as cloud-free as possible. A good site would have skies with less than 15-percent cloud cover for 75 percent of the potential observing period.

Maximum number of hours of astronomical darkness - The prospective site should have long, continuous hours of darkness spread rather uniformly over the entire year. Therefore, if only one site is to be selected, it should lie within latitudes 40°S to 40°N.

Dark sky -Lights from surrounding urban or industrial areas tend to increase the sky brightness to the detriment of good astrometrical observations. Thus, the site should be located away from current or potential land uses which result in the generation of high-intensity surface lighting.

High transparency - The sky at the site should be free from natural and man-made atmospheric pollution. Man-made pollutants could be in the form of smog, haze, smoke, aerosols, etc. Natural pollutants could be in the form of pollen, dust, ash, sand, steam, water vapor, etc.

Minimum optical turbulence (good seeing) -The site selected should be located in a region with a low level of wind activity during observation periods. Winds that do exist at the site should flow over the site in a smooth and laminar manner. A high, fiat plateau may be far superior to a mountain. Site study should include both astrometric study of photographic star trails and correlation studies of arrays of sensitive barometers.

Control of future development of the site and its surroundings to ensure continuation of optimum conditions -Although all the [141] conditions listed above may be satisfied at the time of site selection, it is important that consideration be given to the possibility of future developments which could result in a deterioration of optimum site conditions. An example of an observatory where observing conditions gradually deteriorated due to surrounding development was the Lick Observatory located on Mt. Hamilton in California.

Accessibility - The site should be accessible to the personnel who would use the facility as well as to site-construction workers. Again, high mountaintops may be undesirable. We also will assume that the site selected should be located in the United States.

Ground stability -The site selected should be reasonably free from earthquake and volcanic activity as well as from microseismic activity.

Severe weather -The site should be free from severe weather phenomena such as hurricanes, tornados, typhoons, and duststorms.

Many site surveys have been taken around the world in the last decade. Climatological and seeing conditions at many sites have been extensively surveyed to determine their quality. The seeing was generally measured by use of the polar star trail method developed by Walker. Representative subject sites are shown in a worldwide map (fig. 60).

The high desert country of southwest United States is promising because of the prevalence of clear days and nights, and because of the high elevation with large flat areas. We suggest that the site should be located on a flat-topped mesa flanked by talus slopes for a major fraction of its height to provide a low turbulence atmosphere. We considered the southwestern corner of Arizona in a band with its center at Yuma, running to the north and east of Yuma for a distance of 30 to 70 miles. This area has the highest percentage of clear weather in the United States. In this region, the Kofa Mountains and the Castle Dome Mountains have high plateaus and low potential for future development. A significant portion of this region is contained within the Kofa Game Range, which is under the control of the Federal Bureau of Fish and Wildlife Management and probably would not be a potential site. All lands to the east of the game range...

....are at altitudes too low for consideration. However, a mesa directly to the north of the game range looks promising. In particular, Black Mesa has the following characteristics: (1) an elevation of about 1100 m; (2) a flat portion in excess of 80 acres (100,000 m²); and (3) it is south of an undeveloped road extending southerly from the main highway to within 1-1/2 miles of the easterly summit and within I mile of the westerly summit.

Development of a site requires the following information: geological data including microenvironment or local lithospheric environment; meteorological or atmospheric conditions; and botanic or local ecology. Data from this investigation will be helpful in the final design stages and during operation.

Geological- The type and distribution of geologic materials must be determined in the near vicinity of the interferometer installation. Physical properties of the various materials in both the surficial unconsolidated and uppermost consolidated bedrock must be determined to minimize the natural microseismic motion of the foundation and to maximize the economical use of geologic materials. Rock properties to be determined include bulk density, porosity, saturation, bearing strength, composition, homogeneity, microseismic background, thermal coefficients, sonic velocities, groundwater table, transmissivity, and expansivity. An exploratory drilling program should be undertaken to obtain the necessary geological data.

A seismometer should be installed at the site for complete evaluation of astrometric data after observation begins. If the seismometer were operated for a year prior to the final design stages, it would be an excellent source of seismic data that are essential for detailed structural design of the optical element foundations.

Ambient Earth vibrations, or microseismic motion, are ever present in all natural and man-made structures. The amplitude and frequency of these vibrations vary from locality to locality, depending on numerous variables and natural phenomena. The ground motion can conveniently be recognized and discussed as short-period (>0.1 Hz), storm (0.1 - 0.01 Hz), and long-period (<0.01 Hz) microseisms. Microseismic data are shown in figure 61. Microseismic motion is least well known in the short-period and very long-period range because of the inability of existing seismographs to accurately record both high and low frequencies.

Ground motion arises from numerous natural processes. Causes that have been defined seem to have rather definite characteristic frequencies. The most pronounced type of motion is storm microseisms with peak amplitudes of 30 - 50µm at 6 - 8-sec periods. These originate predominately from storms and atmospheric turbulence....

.....over ocean bodies, nonlinear interaction of ocean waves traveling in oblique directions, and nonlinear interactions of incident and reflected ocean waves near coastlines.

Long-period microseisms have been attributed to motion of ocean swells, direct transfer of ocean wave energy to sea bottoms, and, in some instances, to various meteorological phenomena.

Short-period microseisms are generated continuously by surf, wind, microbarometric oscillations, atmospheric fronts, thunderstorms, volcanic tremors, turbulent flow in rivers, water body noise (where the frequency is a function of water depth), Earth noise (tidal strain, mass movement, expansion, etc.), and cultural noise.

Variations in microseismic motion are seasonally, daily, and intermittently observed The seasonal amplitudes are about 7 times greater during winter than summer at the 8-sec peak and are about [145] 3.5 times greater at the 16-sec frequency. For the northern hemisphere, an amplitude increase begins in August and continues through winter. Daily variations are an exponential function of wind velocities above 4 m/sec (9 mph) and local barometric fluctuations. Because of the ocean wave contribution to microseisms (6 - 8 sec peak), ambient Earth motion diminishes approximately as an exponential decrease in amplitude as distance from the ocean is increased up to about 350 km. Cultural Earth motion due to such sources as cities, motor vehicles, railroads, aircraft, and dams may be significant locally up to 50 km.

Meteorological -Meteorological data should be obtained to provide frequency distributions of precipitation, wind velocity, and direction. Temperature and barometric data are required to ensure adequate thermal stability in the installation and also to provide the correct response time in the mercury base-level system.

Like the seismometer, permanent installation of atmospheric measuring devices should be an early project. This information would be computerized to provide automatic thermal control for the installation.

Botanical- A survey and mapping of the vegetation within 2 km of the site is necessary to ensure a minimum disturbance in natural surface conditions of the installation area. Although vesicular rock is the proposed ground material at the site, a transition must be created which will minimize thermal and meteorological differences between barren and vegetated areas. In addition, a program of vegetation removal, modification, or replacement must be formulated which will minimize the effect of the installation on the local ecology and natural beauty.

To achieve less error in correction for atmospheric effects, it would be desirable to increase the length of the tunnels in the telescopes to about twice the adopted 100-m length. All other components would remain the same size with suitable optical corrections to [146] the contours of the reflecting lens to adjust to the doubled length. The field of view would be reduced to half the diameter, but at the same time the errors introduced by the atmosphere would also be halved, provided the correlation length for atmosphere disturbance (cf. appendix A) is less than 50 m. Studies of that length for various sites and conditions will be needed first.

To reduce the cost of the telescope, all components can be made half size. This would reduce the total cost by one-half or more, possibly to as much as a third. The result would be a much less powerful system for determining star positions. Not only would the field of view be halved, but the light-gathering power would be reduced to one-fourth that for the proposed system.

There are two basic classes of mirror mountings: active and passive. Active mirror mounts are required for large mirrors to minimize the effects of distortion due to gravity, temperature, wind pressure, and other environmental forces. Passive mirror mounts provide support only at the outer edges and so are used only for lightweight mirrors or when distortion is not a serious problem.

In many existing telescopes, the lever system has been used to support mirrors. This has been the practice for about 75 years and has been used with good success. The idea of the lever system is to provide a counteracting force to that of gravity at selected points on the rear surface of the mirror. The reflecting mirror lens of the 200-inch Hale telescope has 36 such support points. Furthermore, the lever systems are placed in weight-reducing recesses behind the mirror surface. The lever system is based on a compound mechanism. An outstanding advantage of the lever system is that it gives a reaction exactly proportional to the tilt angle of the mirror. Also, the system is essentially static and requires no adjustment under operating conditions. It suffers the disadvantages of friction and added weight.

In large mirrors, gravity effects result in distortions; therefore, recesses or voids can be formed in the rear of the mirror body to reduce mirror weight. Another technique would be to break up the [147] single large mirror into two or more smaller surfaces that provide sufficient reflection for the task at hand.

Air bags have the advantage of distributing support over large: areas. Another technique is to form a sealed cavity behind the mirror and support it uniformly by pressure from behind or, in the reverse direction, by a vacuum (assuming the mirrors are not in a vacuum chamber).

A more recent approach is that of a completely active mirror constructed so as to require continuous monitoring of its surface b means of forces provided by mechanical, hydraulic, or pressure techniques. Such a mirror surface would be quite thin and thus incapable of any self-retention of an accurate surface contour.

The large size of the four tracking mirrors presents a formidable problem in positioning and tracking. If the axis of rotation is chosen to pass through the center of gravity of the tracking mirror unit, then there is no need for counterbalancing forces. However, the point at which any given light ray impinges will then move as the tracking mirror moves and any surface imperfections will hinder the detecting process. Thus, the axis of rotation was located on the surface of the tracking hat mirror, resulting in a variable unbalanced moment. The magnitude of this moment is 2800 N^.m at 30° tilt angle and 5300 N^.m at 70° tilt angle. There are three means of overcoming this imbalance: (1) provide a motor of sufficient torque, (2) install s counterweight on an arm, and (3) attach a spring system to provide s counterbalancing moment. The choice made in this project was to select a suitably large hydraulic torque actuator.

The proposed imaging interferometer can be used as a seismic instrument by analyzing the data differently. Astrometry studied differences in star coordinates. Geophysical phenomena are studied by analyzing coordinate sums-the average position of a star field is [148] sensitive to the rotation rate of Earth and to tilts of the interferometer. As a tiltmeter, the ISI would be limited by the recording sensitivity of the detector system and, on the high-frequency side, by the natural frequency of the geologic material upon which it is built or on the frequency of the designed foundation.

We did no detailed study on the use of the ISI in this mode, but a few remarks can be made. Current studies of the rotation of Earth would benefit from more precise transit circle devices, and polar wobble studies would benefit from better declination measurements. Both needs are met by the ISI. As a catalog of star positions for the ISI observation zone is gradually improved, it will become possible to tie together all the observations during a night to study small tilts in the interferometers, both cyclic tilts and tilts of longer trends. Such tilts result, respectively, from tides and lithospheric streams.

The current level of precision (and accuracy) in astrometric observations is significantly poorer than can ultimately be obtained by a ground-based telescope. The ultimate limitation of the precision of ground-based astrometric observations of the type considered here derives from effects due to Earth's atmosphere. For systems that are small to moderate in size (100 m), this atmospheric limitation is at the level of >10^-4 arcsec, a factor of 30 below current precision levels. Whether larger (I km) systems such as that under consideration by Currie and co-workers can further reduce the detrimental effects of Earth's atmosphere is an open question. This factor of 30 can be achieved by utilization of modern technology in conjunction with well-established concepts of telescope optics. The Orion ISI is a novel and complex device that employs state-of-the-art technology and is theoretically capable of attaining 10^-4-arcsec/yr accuracy in relative astrometric observations.

As with any complex instrument, the Orion ISI has both weaknesses and strengths. However, in the admittedly biased opinion of the "Orion people," the latter far outweigh the former. The principal limitations or weaknesses of the ISI are:

[149] 1. Complexity

2. Restriction to relatively bright (m_v +15) stars

3. Restriction to stars that are more than 5 - 10 pc from the Sun.

It is difficult to assess the extent to which the intrinsic complexity of the ISI is a weakness of the system. It must be stressed that the Orion ISI concept is the result of only a few weeks of work, and that quite often the first attempt at design of a novel instrument is much more complex than it need be. Subsequent analysis of the Orion ISI concept may reveal that the essential aspects of the concept can be captured and recast in a less complex (hence more reliable and less expensive) form. The second limitation listed above stems most directly from the requirements for very short (0.1 sec) integration times to minimize atmospheric effects. This limitation is not too severe. The third limitation, the "far-sightedness" of Orion, derives from the fact that the ISI requires fringes to obtain accurate position measures. If a star is resolved by the ISI, it will not produce such fringes. A typical stellar diameter is 10⁹ m (for spectral types G-M) and the resolution of the ISI (= /2B = 5 x 10^-7 m/ 2 x 10² m = 2.5 x 10^-9 rad) is sufficient to resolve 10⁹ m at a distance of ~10 pc (3 x 10^-7 m). in terms of a comprehensive search, this limitation may not be too severe because the ISI could search for planets around stars out to a distance of 30-50 pc, and the number of stars in the volume of space bounded on the outside by a distance of, say, 40 pc from the Sun and on the inside by 10 pc from the Sun is ~4³ = 64 times the number of stars within 10 pc of the Sun.

The principal assets or strengths of the Orion ISI are:

1. Deep space coverage

2. Stable structure

3. Freedom from optical aberrations

4. Large observing field

5: Minimization of atmospheric effects

6. Fully automated operation

7. Real-time data reduction

8. Ultrahigh precision

Asset (1), the ability of the ISI to study stars as far from the | Sun as 30 - 50 pc, is equivalent to saying that the ISI can search a sufficiently large and homogeneous sample of stars to provide statistics on the nature of planetary systems. The highly stable structure (not [150] generally a characteristic for telescopes at this level of stability) means that there are a minimum number of moving key optical components (tracking flats) that are subject to varying gravitational stresses, and also that the thermal environment of the entire system is controlled. The ISI is, in principle, free of those optical aberrations (e.g., coma and astigmatism) that are major sources of astrometric error. The ISI instantaneous]y images a 1-square-degree field of view (2 square degrees during a 5-min observation). This field of view provides typically 10 - 20 simultaneously measured reference stars for any given program star. Measurement of relative stellar positions only in azimuth circumvents many of the detrimental effects of Earth's atmosphere on astrometric observations, principally the refractive effects associated with measurement of relative zenith separation. The fully automated operation of the ISI is not a feature unique to the ISI, nor does it offer any strong advantage in terms of better accuracy. It does, however, provide for relatively straightforward real-time internal monitoring and control of the various components of the ISI.

The capability of real-time, on-line data reduction is an important aspect of the ISI. One of the more tedious and time-consuming aspects of most existing photographic astrometry is the postobservational analysis of the plates. The time delay means that if small error. are present in the output data, they are often not discovered in time to obtain substitute observations. Also, the on-line nature of the primary data reduction eliminates many of the sources of error in positional measurement which can arise when data reduction is per formed through a sequence of data storage/retrieval processes Asset (8) is in large measure a consequence of the other items listed above. However, since precision is the ultimate goal of an instrument it is specifically mentioned here.

Perhaps the best summary statement that can be made as a con sequence of this study is that there is no doubt that proper application of modern technology and optics can significantly increase man's ability to study the position and motion of stars. It is some what ironical that the type of observational work, which until very recently was astronomy, has to a large extent not enjoyed the fruit of modern technology. It is hoped that Project Orion and specifically the concept of the Orion ISI will play a role in redressing this oversight.

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