Moishe Garfinkle
Innovative Optics Group
Philadelphia, PA
(215) 235-5042


Disclosed herein is a conceptual description of a rectangular-aperture astronomical telescope denoted the Scanning Tomographical Imaging Instrument (STII) utilizing orthogonal plano-conical mirrors figured by servomechanical actuators. The sectored reflectors of the STII are fully figured in situ. Accordingly the STII constitutes a decided break with the a priori figured circular aperture upon which astronomical telescopes have relied for some four centuries. Auspiciously, developments in current materials, mechanics and electronics have progressed so far that the most advanced concepts are probably beyond the technological needs of the STII. Because of its linear construction very large increases in extent and resolution are decidedly practical as compared to circular apertures now under consideration or construction. Orbital, lunar and terrestrial mountings are discussed in detail.

Optical Arrangement
Aberration Concerns
Scanning Concerns
Signal Concerns
Noise Concerns
Spectrometric Concerns
Reflector Concerns
Reflector Contour
Reflector Figure
Reflector Material
Structural Configuration
Aperture Size Considerations
In Situ Phasing
Solar Satellites
Quasar Detail
Stellar Photospheres
Faint Companions
Galactic Detail
Extra-Solar Planets

For the past four centuries optical imaging devices in general and astronomical instruments in particular have relied on the circular aperture as the primary light-gathering element. Because the optical elements and ray path are symmetrical about the optical axis the fabrication of the primary reflector, although possibly arduous, is not exceedingly complex, particularly for small telescopes. Moreover, light-gathering power and resolving power, the former proportional to the diameter of the aperture and the latter the circular area, are as intimately related as are the diameter and the area. Consequently for high resolving power large circular reflectors are required. However for very large telescopes, such as those projected instruments with apertures significantly greater than ten meters, the fabrication, alignment and maintenances of the primary reflector becomes prodigious, and in fact borders on the impractical from both economical as well as technical considerations.
In view of this dichotomy, for the next generation of observational instruments this relationship between light-gathering power and resolving power is being partially severed, particularly for orbiting instruments. For significantly greater light gathering power projected orbiting telescopes with large circular apertures will rely on multiple-sectored reflectors servomechanically positioned and aligned, which however can compromise the resolution required for fine imaging. For significantly greater resolving power reliance will be placed on imaging interferometers with dilute apertures on extended baselines (Traub 1984; Shao 1992). These interferometers would have comprised relatively small circular reflectors or a cruciform in various arrangements to ostensibly achieve phase closure. However the point-spread function suffers grievously using dilute apertures, compromising the principal objective of imaging interferometers. Both of these past proposed telescopes would have requires rotation about their optical axes as shown in Figure 1a.
Figure 1a. Mills Cross and COSMIC Aperture Arrangement
Because of practical limitations on fabrication, transport, erection and in situ figure stability, monolithic circular reflectors such as employed by the HST and earth surveillance telescopes will probable not exceed five meters or so. As a consequence of this limitation sectored reflectors such as now employed by the Keck, but such apertures for orbital deployment such as the JWST will probably not greatly exceed ten meters before encountering the same limitations now restricting orbiting monolithic reflectors. In regard to these difficulties inherent to very large circular apertures it is proposed to dispense with the circular aperture entirely and rely instead on the rectangular aperture to obtain very high resolutions without the concurrent requirement for very large reflector areas. Although the optical characteristics of the rectangular aperture have been known since optics had been systematically studied, ostensibly no known imaging devices utilize this aperture. Nevertheless its advantages are manifest.

Figures 2a and 2b illustrate typical circular and rectangular point-source diffraction patterns, illustrating just how fundamentally different imaging using the rectangular aperture differs from that using the circular aperture.
Figure 2a. Typical Circular Aperture Diffraction Pattern
The circular aperture produces a polar diffraction pattern as shown in Figure 2a while the rectangular aperture produces a rectilinear diffraction pattern as shown in Figure 2b.
Figure 2b. Typical Rectangular Aperture Diffraction Pattern
The great advantage of the rectangular aperture over the circular aperture in regard to astronomical observations becomes fully evident in relation to the the Point Spread Function. The rectangular aperture PSF indicates that potentially 95% of the incident flux can be concentrated at the interference-pattern core compared to the roughly 90% maximum for the circular aperture. For the same point source the interference-pattern core is both brighter and narrower for the rectangular aperture.
Figure 2c. Relative Point Spread Functions
It is evident that the rectangular aperture has decided advantages over the circular aperture on theoretical grounds alone in regard to both image contrast and resolving power. To exploit these advantages however requires that the utility of the rectangular aperture be considered on practical grounds.

To circumvent the problem that the rectangular aperture projects a rectilinear diffraction pattern rather than a diffraction disc two primary rectangular apertures are employed; orthogonal to each other, and each orthogonal to the optical axis. Because the incident flux focused by rectangular apertures with this configuration does not follow equivalent paths in the tangential and sagittal planes the convention shown in Figure 3a will be followed in describing the optical arrangement. The tangential and sagittal directions referred to in the description of the rectangular aperture are perpendicular to the planes shown, respectively, and are mutually orthogonal to the optical axis.
Figure 3a. Orientation of Tangential and sagittal Planes
For exegetic purposes an instrument comprising only a primary tangential and sagittal aperture is shown in Figure 3b. These comprise plano-conic reflectors with orthogonal axes of curvature.
Figure 3b. Orientation of Tangential and sagittal Planes
The tangential reflector focuses solely in the tangential plane and the sagittal reflector in the sagittal plane. Figure 3c illustrates the projected diffraction pattern. The projection is distinguished by the rectilinear null bands.
Figure 3c. Combined Tangential and sagittal Diffraction Pattern
The rectangular aperture is unique in that, regardless of its configuration or ratio of its sides, a full Point Spread Function (PSF) is recovered (Stockman 1996). In the case of the circular aperture only for a Filling Factor of unity is the Speed Factor unity as seen in Figure 3d, and only for a Speed Factor of unity is a full PSF recovered. In the case of the rectangular aperture the Speed Factor is unity independently of the Filling Factor, so therefore the full PSF is recovered independently of Filling Factor, and consequently independently of its configuration or ratio of its sides.
Figure 3d. Relative Speed Factors
Summing up the advantages of the rectangular aperture for astronomical imaging:

To exploit the remarkable advantages of the rectangular aperture for astronomical imaging the Scanning Tomographical Imaging Instrument (STII) was conceived and is described herein. The eminent optical engineers Daniel Schroeder, author of Astronomical Optics 2000, and Raymond Wilson, author of Telescope Optic 1999, are familiar with the optical arrangement of the STII and they have indicated that the rectangular aperture would be well suited to the construction of telescopes with resolving powers far beyond those presently envisioned.

A practical 25-meter STII would comprise a series of plano-conic reflectors that are fully servomechanically figured to conic curvatures and positioned in situ, dispensing with a priori mechanical figuring. Hence the STII constitutes a decided break with the fully or partially filled circular apertures. The arrangement of the principal plano-conic reflectors for an aplanatic STII optical system devised by Moishe Garfinkle is shown in Figure 4a.
Figure 4a. Plano-Conical Optical Elements of the STII
According to this optical arrangement the axes of curvature of the reflectors are mutually orthogonal to the optical axis; all reflectors are plano-conic; and the reflectors are fabricated and erected essentially as flats and fully figured solely by actuators. For simple one-dimensional curvature the focusing and phase aligning algorithm would be comparatively simple compared to the two-dimensional Keck algorithm. One of the most important considerations in dimensioning the STII is that resolving power and light gathering power are now divorced. The tangential extent of the STII reflectors determines resolving power while the sagittal extent determines light-gathering power.
Because the ray traces in the tangential and the sagittal planes follow non-equivalent paths they must be considered separately. Hence two ray trace diagrams are required: shown in Figures 4b and 4c.
Figure 4b. Ray Traces in Tangential Plane for an Aplanatic Optical Arrangement
The rays are focused in the tangential plane by the primary tangential reflector and the secondary tangential reflector as shown in Figure 4b. From the secondary tangential reflector the rays travel to the primary sagittal reflector. The rays are focused in the sagittal plane by the primary sagittal reflector and the secondary sagittal reflector as shown in Figure 4c. Hence the rays are fully focused in both the tangential and sagittal directions, but only in the tangential plane is the 25 meter resolution realized.
Figure 4b. Ray Traces in sagittal Plane for an Aplanatic Optical Arrangement
To cover the entire object field at full resolution the STII is rotated about its optical axis, with a sufficient number of discrete exposures required to recover the full wavefront. As a full aperture instrument the STII can recover a continuous wavefront as does the single circular aperture. Hence the signal-to-noise ratio (SNR) of the STII will be superior to any dilute arrangement, a necessity in imaging details on extended sources. Using computer tomographical deconvolution the object field is reconstructed from the discrete exposures at full resolution.

Figure 5a illustrates the object plane occupied by a simulated 15th magnitude quasar and below that the image projected on the focal plane of a 25-meter STII at each angle about its axis of rotation at which an exposure is made. Although full resolution is obtained in the tangential direction each exposure is effectively smeared in the sagittal direction. Nevertheless the full wavefront is recovered in both directions for every exposure and accordingly no wavefront reconstruction is required, greatly simplifying Computer Tomographical (CT) deconvolution. Accordingly none of the information required to fully recover the object field projected on the focal plane is lost, it solely needs reconstruction.
Figure 5a. Image Projection at Several Angular Exposures
In practice the conventional CT analysis used in ordinary medical diagnosis for body section analysis is all that is required for image deconvolution of the projections (Bracewell 1979). Because an image plane rather than a body section is dealt with, all that needs to be considered are intensities in two-dimensions rather than three-dimensions as in medical practice (Herman 1980). For tomographical analysis to be practical however the information gathered at each scanning angle Z of the STII about its optical axis must be reduced to a form that emulates the profiles shown from CT body-section analysis. This reduction is accomplished by summing all of the optical densities at each pixel array at the image plane in the sagittal direction as shown in Figure 5b/s. This operation is performed at each scanning angle Z of the STII, with angle Z equivalent to the rotation angle z of a CT scanner in a body section analysis. The result is an array of projections in the tangential direction as shown in Figure 5b/t at each angle Z examined.
Figure 5b. Image Reduction at Focal Plane for Each Angular Exposure
An STII simulation conducted by the Medical Imaging Processing Group at the University of Pennsylvania confirms the viability of the CT analysis. By using an Expectation Maximization procedure a series of object field images as might be recorded by a rotating STII was deconvoluted from simulated STII exposures reduced to projections as shown in Figure 6b. Because wavefront reconstruction was not required, the superior rectangular aperture PSF was preserved, thereby permitting secondary maxima to be ignored. The Medical Imaging Group deconvoluted the object field image with near perfection without any knowledge of the STII simulation algorithm originally used to convolute the object field images.

Optical Arrangement
In present practice the optical arrangement to be selected for a telescope is among the initial concerns that must be settled before the mechanical and electronic concerns can be addressed. Table VI lists four optical systems that have been employed in conventional astronomical telescopes (Schroeder 1987). Because the reflectors are symmetrical about their optical axis their tangential and sagittal figures are identical.
Table VIa. Conic Constants for Telescope Reflectors
Whereas the optical arrangement must be decided upon a priori  for a conventional telescope, for the STII any of the arrangements listed can be realized in situ, or others that might be developed specifically for the STII. Likewise the focal lengths can be varied in situ for any of these figures. Essentially, what is at present a hardware concern becomes for the STII a software concern. Inasmuch as the STII reflectors have only one-dimensional curvature - the value of the conic constant K can be varied within the mechanical limits of the servomechanical actuators which figure the primary and secondary reflectors.
Aberration Concerns
As in circular aperture practice, the extent of the STII field will depend on the effectiveness of practical aberration correction techniques. Inasmuch as the STII employs at least two reflecting ribbon surfaces in each of the tangential and sagittal planes which are figured in situ to any required plano-conic curvature for these reflectors can be programmed for aberration correction. Of course no aberration corrections are required in the sagittal direction as sagittal image resolution is not relevant in reconstructing the final image.
Scanning Concerns
Some image smearing will occur at the image plane inasmuch as the STII rotates relative to the object plane. The degree of smearing will depend primarily on the angular extent of each exposure. However, as seen from Figure 5b, the charges accumulated on each pixel of the detector for each exposure are integrated in the tangential direction, resulting in a relatively high charge count for each projection, thereby reducing the individual exposure periods. Smearing moreover can be minimized if the detector were rotated to keep it aligned with the objective field during each exposure, with the detector returning to it initial position at the start of the next exposure.
Signal Concerns
Unlike conventional telescopes, the image produced by the STII comprises many discrete exposures, ostensibly indicating that very long exposure periods would be required for a complete image. Again, the charges accumulated on each pixel for each exposure are integrated in the tangential direction, resulting in a relatively high charge count for each projection, thereby reducing the individual exposure periods.
Noise Concerns
In large measure the imaging capability of the STII will be limited by the SNR of the detector output. This source of this limitation can be external (background light, random wavefront errors) or internal (reflector aberrations and asperities, detector dark count and read noise).
Detector dark count and read noise are persistent problems, and because the final image comprises many exposures, might degrade STII performance. Alternative detector configurations might be considered. Because the charges accumulated on each pixel for each exposure are collected in the tangential direction, a detector with elongated pixels as shown in Figures 6a might serve equally well: potentially reducing both the detector dark count and detector read noise compared with a full array of pixels while maintaining the tangential resolution. Alternatively, the incident flux might be projected on a narrow detector as shown in Figure 6c while maintaining the tangential resolution. The projections 6b and 6d are identical. The practicality of this scheme has not been investigated.
Figure 6. Alternative Detector Configurations
Because the STII can be refigured in situ the optical arrangement of the STII can be optimized by judicious choice of optical arrangement and detector to minimize noise for the instruments involved, such as wide field or faint object cameras. However, the primary reflector of the STII is segmented, which has the potential of degrading the PSF, which is equivalent to diminishing the SNR. The segment edges diffract incident light into complex patterns which appear as secondary maxima at the detector. If the distance between adjacent segments were less that the incident wavelengths of interest, this problem would be minimal, but this solution would probably be mechanically impractical. Apparently the solution is to maximize the area of each segment to minimize the number of segments and therefore the edge length.
Spectrometric Concerns
As for spectrometric analysis of the image detected by a rotating instrument such as the STII, analysis of point sources on the optical axis is hardly influenced by rotation. Spectrometric analysis of extended sources is another matter. For each exposure all of the detector pixels in the sagittal direction are summed for tomographic deconvolution as shown in Figure 5b. If this summation is performed optically the result is a narrow full wavelength band in the tangential direction at the image plane for each angular exposure. If this band were to be scanned in the tangential plane and the light transmitted to a spectrometer, the result would be a series of spectral analyses in the tangential direction for each angular exposure, one for each bandwidth. When the exposure for each spectral band for each angular exposure is independently deconvoluted the result would be a spectrometric map of the extended source.
For true-color camera renditions of extended sources alternate angular exposures would be made each using appropriate color filters. These would be tomographically deconvoluted separately and the three color images then superimposed as in conventional practice.
Diffraction Concerns
Unlike terrestrial telescopes wherein diffraction irregularities arising from edges, gaps and asperities are averaged because of atmospheric seeing, this is not the case for the STII.
Two parameters can be used to characterize the diffraction image:
1. The fraction Edif of the energy incident on the primary that is diffracted by the gaps:
Edif= area of gaps/area of primary
2. The angular scale Adif of the diffraction pattern:
Adif = wavelength/width of gaps
Assuming a gap width of 7 mm as in the case of the Keck then the total gap area would be 0.34 m2.
Table VIb. Comparative Diffraction Parameters
It is apparent from Table VIb that the diffraction image of the STII is comparable to that of other large telescopes.

Reflector Contour
Developments in current materials, mechanics and electronics have progressed so far that the most advanced concepts are beyond the technological needs of the STII.
Table VIIa. Reflector Specifications
The STII reflectors are fully figured using servomechanical actuators. As an example consider a 25-meter primary aperture as specified in Table VIIa and illustrated in Figure 7a.
Figure 7a. Primary Reflector Contour
The reflector contour depends on the extension of each actuators. As illustrated in Figure 7b, the difference between a circular contour and a parabolic or hyperbolic contour is only several millimeters, permitting full in situ figuring.
Figure 7b. Deviation of Hyperbola and Parabola from Circular Contour
Each of the twelve sectors are peripherally supported by linear arrays of actuators, as shown in Figure 7c. The maximum surface elongation of the sectors is in the microstrain range, minimizing reflector surface distortion.
Figure 7c. Sector Contour
Surface distortion can arise from two sources: elastic deformation and point-loading by the actuators.
The plano-conical surfaces of the STII are stiff against two dimensional curvature, exactly as required to permit a relatively small number of low-force peripheral actuators to handle the full correction requirements. In contrast the circular aperture first requires a figured reflector that must subsequently be corrected in situ in two dimensions, requiring that actuators be placed in close proximity to one another across the back surface of the reflector for figure correction. In this regard it would be instructional to compare the rectangular aperture of the STII with an equivalent circular aperture instrument, both designed for orbital placement.
Table VIIb. Aperture Comparison
For example, an orbital 8.9 meter diameter telescope with two-mm thick sectors would probably require more than 6500 actuators some ten cm apart in order to continually correct the 18 reflectors figured in two dimensions. Unlike the Keck with its 75 mm thick fully-figured sectors, the orbital sectored aperture will not only require on-going focusing corrections for tilt, tip, and piston, but the sectors will require simulataneous figure corrections.
In contrast a two mm thick 1.25m x 4m rectangular sector with peripheral actuators five cm apart would require not quite 200 actuators. The 12 sectors would require almost 2400 actuators for the STII 62.5 m2 primary tangential aperture. Because any tendency to compound curvature of the plano-conical reflectors would increase the load on the affected actuators, force discrepancies detection as well as optical detection of any such occurrence would be practical.
Reflector Figure
Both Shack-Hartmann and curvature sensing have been used to great advantage on the Keck segmented reflector(Chanan 1998). Because the mirrors of the STII are in situ figured full-surface phasing of each segment is a natural application of the Shack-Hartmann technique, rather than being a corrective measure as regarded in present practice, greatly simplifying phasing requirements. Both alignment detectors and servomechanical actuators are orthogonally positioned as shown in Figure 7d to align the sectors within a fraction of a wavelength: at least l/10.
Figure 7d. Orthogonal Displacement Detectors
The Shack-Hartmann lenslets positioned at strategic positions on each rectangular sector STII permits active figuring to be significantly simpler than the non-orthogonal requirements for each of the hexagonal complex-curved sectors of circular aperture instruments as shown in Figure 7e. Hence the control circuitry and algorithm for active rectilinear optics correction would be significantly simplified, an important consideration for orbiting instruments in terms of computational limitations.
Figure 7e. Hexagonal Displacement Detectors
Beyond figuring corrections, advantages would accrue by applying adaptive optics to the STII configuration to correct for normal surface asperities in the primary and secondary mirror which scatter reflected light (Shao 1996). Assuming that the effect of such perturbations are similar to the effect of turbulence-induced anisoplanatism on terrestrial telescopes, this task can be accomplished by using a deformable mirror to correct for wavefront distortions, significantly diminishing such scattering (Welsh 1991). Again, corrections would be required only in the tangential direction, greatly simplifying the mechanical arrangement and the correction algorithm.
The simple-curvature STII mirrors would be ideal for figuring by support actuators that could be clamped after in situ figuring, reducing power drainage (Bamford 1996). Piezoelectric strip transducers secured to the underside of the mirrors could be then used for continuous fine-figuring corrections (Kuo 1992).
Figure 7f. Piezoelectric Reflector Figuring
Though designed for hexagonal mirror sectors as shown Figure 7f such tranducers would be more applicable to the rectilinear arrangement of the STII for 1) compensation of residual stresses, 2) compensate for temperature variations and 3) corrections for gravity-vector alignment.
Reflector Material
Reflector construction materials can be either polymeric, ceramic or metallic, each with specific advantages. Composite mirrors comprising hybrid fibres would be ideal for the deformable mirrors of the STII. For example, mirror construction using together graphite, glass and kevlar fibres with an epoxy and cyanate ester matrix results in a highly stable orbital reflector lighter than glass at only 1.8 Mg/m3 and already proven in practice (McConnell 1996). The high-modulus graphite fibres would be oriented parallel to the axis of curvature of the reflectors. In all probability the fibre architecture would be strictly orthogonal, without bias fibre orientations. With in situ figuring the STII is simply an assembly of discrete components whose final optical alignment after erection can be conducted servomechanically. The result would be a significant weight advantage over glass at 2.2 Mg/m3. Another candidate, albeit more dense at 2.7 Mg/m3 but with a thermal conductivity orders of magnitude greater than other candidates, would be nickel-plated aluminum. This material can take a very fine polish and has been successfully tested in orbit aboard surveillance satellites. Beryllium is another contender with a density of just 1.8 Mg/m3 and is a material actively being pursued for future telescopes. Magnesium (1.7 Mg/m3) is another contender with its high modulus.
Structural Configuration
Because the STII is configured so radically different from conventional telescopes it is worthwhile considering a possible construction as shown in Figure 7d for an Xt=25 meter instrument with an aspect ratio Xt/Xs=10. The HST shown for comparison.
Figure 7g. Possible Configuration of a 25-Meter Aperture f/1.5 STII
The STII cage construction has no support braces across the active face of the primary reflector to obstruct the light path and complicate the point spread function, thereby eliminating diffraction errors from this source. Such errors can obscure faint sources, a particular difficulty when milliarcsecond resolutions are sought (Roddier 1981). The primary aperture shown comprises 12 identical 4 x 1.25 meter simple-curvature rectangular segments for a 25 x 2.5 meter tangential-aperture instrument.
The STII cage can be significantly lighter than that required for conventional telescopes inasmuch as the optical elements are narrow in the sagittal direction, permitting a compact structural arrangement. Moreover, with advanced circular-aperture telescopes approaching f/1.0, significantly faster apertures are a distinct possibility, further lightening the STII cage.
The reflector outriggers shown in Figures 7d and 7e would be a conventionally fabricated space-frame constructed in the usual manner onto which the reflector actuation frames are secured.
Figure 7h. Possible Configuration of STII Reflector Outrigger
The primary reflector sectors secured to their rigid actuation frames might be transported as separate units in a transport module, perhaps as shown in Figure 7f.
Figure 7i. Possible Configuration of STII Reflector Outrigger
The actuation frames would then be positioned and secured on the prepared reflector outriggers.
Figure 7j. Primary Reflector Sectors Secured to Outrigger
In Situ Phasing
Fully phasing a telescope primary aperture by remote control will be an unprecedented task. Fortunately full sagittal focusing is not required for the STII, only that the intensity peak of the saggital flux band be essentially centered on the detector. The Keck experience would be invaluable for this endeavor (Chanan 1998).
Tangential focusing utilizing a stellar point source can be accomplished in phases. Preliminary focusing would involve only the four outer sectors with the remaining sectors deliberately defocused. With the actuator positions recorded the outer sectors would then be defocused. This process would then be repeated with the four middle sectors and finally with the four inner sectors, recalling from Figure 3d that each group of four sectors is in itself a complete optical system. With preliminary focusing completed and sector piston corrections made using edge position transducers all of the sectors would then be readjusted for final fine focusing.

There are three possible placements of the STII as an orbiting telescope. Two are of course the Lagrange points, either the L1 earth-moon or the L2 earth-sun. In terms or reparability only the L1 point would be practical.
With its high light-gathering power a solar orbit between Earth and Mars would probably suffice as far as science requirements are concerned, despite interstellar dust interference. Inasmuch as the STII is in continuous rotation about its optical axis, power, control and telemetry continuity ostensible might be difficult to maintain. A possible solution would be utilizing a module equipped with solar panels and directional antennas, maintained in close proximity to the STII as shown in Figure 7d. Microwave power transmission to the STII would keep on-board batteries charged and the module would comprise a relay station for control and telemetry. Nevertheless there are innumerable problem associated with this solution.
Alternatively, the STII would be an ideal instrument for a lunar observatory on the reverse side of the moon, probably an elevated equatorial site. Dispensing quickly with the obvious disadvantage: the instrument could only be used for observations for perhaps ten earth days during each lunar night: roughly equivalent to the same monthly viewing period for terrestrial telescopes, consider however


All existing and projected terrestrial telescopes, whether monolithic, segmented or multiple aperture, are based on the circular aperture. To determine the feasibility of the rectangular-aperture STII let us compare it to the projected TMT, a joint project of the Association of Universities for Research in Astronomy and the California Extremely Large Telescope Development Corporation. They agreed on a 30-meter segmented aperture instrument. Evidently the objective of the 30-meter aperture project is a diffraction-limited device with the greatest practical light-gathering and resolving power. The greatest limiter on these specifications are technical practicality, seeing constraints and financial availability, all in fact dependent on each other.
The principal decision as to the optical and mechanical properties of the hexagonal sectors is most critical. Either the sectors can be rigid and fully figured as is the Keck or flexible and in situ figured as will be the JWST. In either case the complex curvature of each sector, its figure depending on its aperture position, entails a considerable undertaking. Equally important, the accuracy of figuring for each sector will determine the wavelength band of the instrument. Both the JWST and the TMT are proposed as infrared instruments.
The light-gathering power of the circular aperture is proportional to the aperture area and the resolving power on the circular diameter: 705 m2 and 30 m respectively. Using the same aspect ratio of 10:1 of a future STII as specified previously to achieve an equivalent light-gathering power then the dimensions of the ground-based STII would be roughly 85 meters in the tangential direction and 8.5 meters in the sagittal. Its diffraction-limited resolution however would be almost three times that of the TMT . Of course to realized a future STII resolution beyond seeing limits the wavefront correction must be of the highest order. Figure 8a shows the comparable dimensions. Whether or not the STII resolution can be extended into the visible range by at least l/10 figuring is problematic although with the rectangular aperture l/4 is a distinct possibility worth considering.
Figure 8a. Dimensional Comparison Between the TMT and the STII

Of course these dimensions are based on simplistic assumptions but the general considerations are valid. Most importantly the STII uses orthogonally positioned simple-curvature reflectors with far fewer electromechanical actuators than would be required by a circular aperture. The structures are compared in Figure 8b.

Figure 8b. Structural Comparison Between the TMT and either the Lunar or Terrestrial STII

The high light-gathering power of the STII, almost three magnitudes greater than the Hubble, will permit detection of astronomical objects far dimmer than possible by any projected orbiting observatory. A 25-meter STII would have a full-wavefront resolution almost ten times better than the Hubble, particularly useful for extended-source imaging.
Solar Satellites
Planetary or satellite rotation or atmospheric turbulences will not blur exposures as each exposure would be several magnitudes shorter than the blur time at 500 nm.
Quasar Detail
Figure 9a illustrates a simulated 15th magnitude quasar, which also illustrates the resolution limitations of present telescopes compared to a 25-meter instrument (Meier 1991).
Figure 9a. Comparison of Diffraction-Limited Resolution for Several Apertures
With its exceedingly high light-gathering and resolving power the STII would be an outstanding instrument for the detection of Cepheid and RR Lyrae variables within very distant galaxies, if in fact any exist in such early galaxies. Independent distance calibration of these variables would of course not be possible, but if there is sufficient confidence that such early variables are similar to more recent variables distances could be estimated with considerable assurance, particular important in refining the red-shift - distance relationship upon which Hubble's constant depends.
The STII would be particularly useful in astrometry, permitting significantly more accurate measurements of variations in proper and radial distances between celestial objects over a volume significantly greater than previously attained, particularly important in detecting variability with distance in the expansion rate, a most important factor in determining the probable age of the universe.
The STII would be ideal for measuring the relative angular dimension of standard objects at known distances, systematic deviations from linearity indicating the magnitude of spacetime curvature, if any. Spacetime curvature depends on the mass density of the universe, and should indicate whether closure will occur, or alternatively that the universe will expand indefinitely. If curvature is greater than baryonic density measurements would indicate, this discrepancy would favor the argument that cold dark matter is an important constituent of the universe.
Stellar Photospheres
The most exacting application of the STII would be the direct resolution of photospheric features on giant and supergiant stars, a distinct possibility with the STII as shown in Figure 9b (Dupree 1984). With its five mas resolution high SNR photospheric features such as convection cells on a Ori, o Cet, a Sco and a Her should be readily discernible by the STII, and perhaps on smaller bodies such as b Peg, a Cen B, and a Boo. Large convective structures on the Cepheid variable d Cep should be resolvable. Spotted stars, such as AR Lac and 5 Cet, probably could not be resolved at photospheric level. However should magnetically-guided chromospheric structures reach lengths perhaps 10 times the stellar radius these possibly could be resolved by the STII. As for flare stars, should flares reach a cross-line-of-sight extent of the order of 20 times the stellar radius the evolution of some such flares should be discernible.
Figure 9b. Stellar disk Resolution of Several Operating and Projected Telescopes
Faint Companions
The observation of faint companions is ordinarily complicated because of diffraction by the support structure of the telescope securing the secondary mirror (Woolf 1982). However without any support structure obstruction in the STII optical path diffraction effects are eliminated from this source. Moreover without support obstructions orbits of such close binaries as b Per and b Lyr and of almost all close binaries with periods greater than 15 days are most probably resolvable. Close binaries with periods less than one day would probably not be resolvable. However only actual observations could answer this question.
Galactic Details
The STII would be particularly suitable for discerning galactic details required in understanding galactic evolution, and perhaps for better ascertaining the nature of galactic cores. As is generally the case however, the instrument itself will reveal hitherto unexpected observations, particularly if direct evidence is observed for the presence of black holes.
Extra-Solar Satellites
Many extra-solar dark bodies have been detected from observed periodic perturbations of parent stars about their mean position.(Marcy 2002) There are now being designed or built various instruments to expand the detection of extra-solar planets. These include Corot, Kepler, JPF and TPF, SIM and Darwin. They rely on either measuring stellar oscillations or relying on an array of interferometers for imaging, flying in formation but physically independent.
About 55 Cancri alone three such bodies have been detected by this oscillations and these appear to have the near-circular orbit characteristics generally associated with solar planets. Figure 9c is a schematic representation of the relative orbits of these three giant planets computed from the perturbation data, presumably gas giants. The outer planet is roughly the size of Jupiter.(Butler 2002) For scale the orbits of the five inner solar planets are superimposed on the orbits of the Cancri planets.
Figure 9c. Presumed Orbit of Planets Orbiting 55 Cancri
The most direct evidence that a dark body detected by perturbations of a parent star is in fact a planet is the partial occultation of HD 209458 detected by optical means (Henry 2000) during precisely the period predicted from perturbation measurements.
That it will be possible to image Jupiter-size planets revolving about sun-like stars with the STII is a distinct possibility although the brightness of the central star overwhelms any images of planets. There are various schemes available to lessen this effect. The two most promising are coronagraphy and interferometry.
The outer planet c is sufficiently far from 55 Cancri that it should be readily detectable by the STII because of the combined high-resolution and high light-gathering power of the instrument. In general however the direct observation of non-solar planets is difficult because of the scatter of light within the instrument from the bright central object obscures such bodies. Adaptive-optic mirror correction could significantly reduce such scattering from reflector surface asperities. (George 2002) Nevertheless success could not be assured unless effective coronagraphical means could be developed to significantly diminish the apparent flux intensity of the parent star represented in Figure 9d.
Figure 9d. Known Planets Orbiting 55 CanCri
To detect the inner planets would require that the parent star be significantly occulted. The best possibility in this regard would be the apodied Lyot Stop (Itoh 1998). As adapted to the STII the star's image is blocked by a narrow occulting ribbon (about the star's size) at an intermediate focal point. The Lyot occulting ribbon is a sort of thread-width sagittal field stop located at a non-virtual pupil position beyond the field stop and before the final focal plane.
Figure 9e. STII Observation of Planets Orbiting 55 CanCri
With the star occulted possible earth-type planets such as b1 , b2 and b3 would be readily detected as shown in Figure 9e, considering the resolution of the STII at just five milliarcseconds. With this resolution atmospheric detail could be determined and orbital detail computed. Moreover, if earth-type planets are present they would be readily detected by the STII with their brightness depending on their albedo. Of course if there are dynamic perturbations in the motions of b and c they could destabilize the orbits of any earth-type planets between them, probably removing them entirely from any habitable zone of the 55 Cancri system.
Interferometry in contrast would require two 25-meter STIIs locked together with perhaps a 100-meter separation with parallel optical axes and aligned tangential axes. The twin STII would revolve about its center-of-gravity parallel to its optical axes.

To observe a planet the size of Earth using a single telescope would require a mirror as wide as a football field -- and it would have to be deployed in space. While that approach is obviously impractical, technologists are rapidly developing more feasible methods of studying such extremely faint objects. Just how obviously inpractical is it?
Because its reflectors are all plano-conic sections building a larger STII by sector addition, at least the size of a football field, can be quite feasible because the STII does not involve redesigning the basic optical system. Although the STII support structure must be redesigned to accommodate the enlarged aperture both along the optical axis and normal to it this is essentially a linear structural engineering problem. Existing composite smart materials will be particularly useful, such as magnetostrictive actuators and quasi-unbalanced architecture that will keep structural beams aligned despite centrifugal loading and transient gravitational gradients.
While figured mirrors are not required, computer capacity is. Not only must the outrigger structure be continually aligned, so must the mirror sectors. While correction algoithms are still simple and orthogonal, massive computer capacity would still be required. What is very much within present capacities is the optical, mechanical and electronic systems.
With state-of-the-art engineering materials and in situ fabrication techniques the development of STIIs with apertures greater than 250 meters becomes a distinct possibility, if not probability. The results would be resolutions ten times that of the 25-meter instrument: some 500 mas while recovering a full PSF. Achieving this resolution should be far easier than maintaining a formation of interferometers flying independently while holding submicrometer alignment in transient gravitational gradients.
In appearance the 250-meter instrument would still somewhat resemble the 25-meter instrument as shown in Figure 10a with the HST for comparison. Recall that in dimensioning the STII resolving power and light gathering power are divorced. The tangential extent of the STII reflectors determines resolving power while the sagittal extent determines light-gathering power.
Figure 10a. Possible Configurationof a 250-Meter Aperture f/1 STII
The resolution of such an instrument is awesome. The disc of red giants could be resolved in detail and a G2 star such as our sun could be resolved at a distance of perhaps 50 parsecs with any Jupiter-size planets visibly detectable.
Figure 10b. Resolution of a 250-meter STII at the distance of 55 Cancri
Depending on their albedos, the presence of satellites about non-solar planets could probably be detected. The 500 mas fiduciary line indicates the extent of resolution of a 250-meter STII. Not only would details of the star 55 Cancri be resolved with coronagraphical techniques, but with computer enhancement that of the outer planets.

There are of course risks involved in undertaking a preliminary analysis of an astronomical instrument that constitutes a decided break with Galileo and Newton and consequently lacks the evolutionary foundation established by these pioneers whose basic design of the astronomical telescope has withstood the test of four centuries. Although much conjecture has been involved in this descriptive report, because of the profound advantages of the rectangular aperture compared to the circular aperture for high-resolution observations it is contended that on a cost-benefit basis a preliminary analysis would be worthwhile to ascertain the fundamental parameters required to adapt the rectangular aperture to astronomical observations.

Innovation/STII Home Page