The Hubble Space Telescope suffers from significant spherical aberration and does not give the predicted diffraction limited images. A maximum of about 15% of the light from a point source is concentrated in a 0.1 arcsecond radius, where 70% was expected. The images consist of this core, surrounded by a complex 4 arcsecond diameter inner halo that contains most of the light and is caused by portions of the primary mirror that are not focussing correctly.  Ground test results uncovered by the Allen commission agree with results derived from studies of the on orbit imagery.
Optical tests on the observatory and examinations of ground tests and equipment used in the primary mirror fabrication  have clearly demonstrated that HST suffers from spherical aberration.  Light striking near the edge of the primary mirror  is brought to a focus about 40 mm behind the focus of light passing close to the secondary baffle. The result is that no choice of focal plane yields the expected diffraction limited images. 
Image quality is also critically dependent on the pointing control system.  FGS and gyro data show that the spacecraft undergoes two periods of particularly large  amplitude pointing excursions per orbit, associated with sunrise and sunset. These excursions are typically 150 milliarcseconds amplitude peak to peak. Throughout the orbit there are additional random episodes of increased jitter, with amplitudes of 15 to 30 milliarcseconds. During quiescent periods, the spacecraft achieves a stability of about 7 milliarcseconds RMS, but falls far short of the top level specification which required that such performance be maintained for 24 hours. Flight software changes are planned that may improve the performance. Further, the FGS are presently not guiding well on stars fainter than 13th magnitude, perhaps as an indirect result of the spherical aberration.  HST was expected to guide on V=14.5 stars. As a result  there is currently a loss of sky coverage at high galactic latitude, especially for the Wide Field Planetary Camera (WFPC). .
The Optical Telescope Assembly (OTA) contains  a 2.4 m diameter  F/2.3 hyperbolic primary mirror, separated from the hyperbolic secondary by 4.9m (Burrows 1990). In the design, the conic  constants on the primary and secondary mirrors are chosen to yield zero third order spherical aberration and field coma.
The secondary mirror can be precisely positioned with 6 degrees of rigid-body freedom to collimate the telescope. Three radial shearing  interferometers called wavefront sensors are located at the inner edges of the FGS fields of view. They were designed to measure the wavefront and allow accurate collimation, but their performance is degraded by the spherical aberration, as a result most of the diagnosis, focussing and collimation efforts have had to rely on anaylsis of the imagery from the SIs.
Behind the primary mirror are 24 force actuators arranged in two concentric circles. They can be used to make small adjustments to the mirror figure, but do not have sufficient dynamic range to correct the spherical aberration.
The on-axis image was expected to  have wavefront aberrations totalling about 1/20 wave rms at 633 nm. The conventional definition of  'diffraction limited'  is that the ratio of the peak of the Point Spread Function (PSF) to the theoretical limit in the absence of aberrations  (Strehl ratio) be greater than 0.8, corresponding to a wavefront error of  better than 1/14 wave rms. By this definition, HST was expected to be diffraction limited at wavelengths above 445 nm. .
The WFPC (Griffiths 1990) reimages the OTA focal plane.  A four-faceted pyramid divides the field into one of  two possible sets of camera modules, the F/12.9 Wide Field camera (WFC) and F/30 Planetary Camera (PC). The  pyramid is rotated by 45 degrees to  switch between cameras. In each mode, the four beams are separately folded and then reimaged by four small Cassegrain  repeaters onto thinned, backside illuminated, Texas  Instruments 800x800 CCDs, with 15 micron pixels. 
The secondary obscurations  in the WFPC repeaters are not in the telescope pupil, and therefore, vignette the beam in a field dependent manner.  At the center of each chip, the obscuration should be centered over the OTA secondary obscuration, and moves in a linear manner with field position. Images of crowded star fields show that the obscuration is not centered at the center of the chip presumably because of internal misalignments. Instead the obscuration pattern appears symmetrical about a point that varies for each camera repeater, but is typically 200 pixels from the center of the chip.
An indication of the serious problems with the HST optics came with the first light image in the WF camera. The image had a tight core containing about 10 percent of the light, a surrounding plateau exhibiting  a curious 'kidney' shape containing most of the energy, and 'tendrils' extending in apparently random directions from the plateau. The images were not consistent with those expected from a defocussed and uncollimated telescope.  The reason is that the HST images suffer from spherical aberration.
The model fits to the camera images show that HST suffers from about -0.43 waves rms of spherical aberration at 633 nm. The error corresponds to a 4.6 micron optical path length error for marginal rays at the paraxial focus, a 1.6 arcseconds diameter circle of least confusion, a 2.3 micron surface error at the edge of the primary, or a change of the primary mirror conic constant from the specified -1.0022985 to about -1.014. The marginal focus is about 43 mm from the paraxial focus in theF/24 focal plane. The 'best focus' images were taken about 12 mm from the paraxial focus. Moving closer to the diffraction focus or to the circle of least confusion causes the outer halo to decrease in size but also causes the the encircled energy within 0.1 arcsecond to fall by about 40%. 
The Strehl ratio of HST was predicted to be 0.8, it is an order of magnitude lower, but still an order of magnitude higher than the value for 0.5 arcseconds ground-based seeing through the same telescope.
Most of the energy is contained within the geometric image, but some is scattered to still larger angles by mirror microroughness and diffraction on the HST pupil. This scattering  appears lower than prelaunch predictions based on the primary mirror measurements (Schroeder 1987, Burrows 1990), although it is difficult to define the sky level in the data, and so the estimates of encircled energy beyond the geometric image are very uncertain.
The spherical aberration is known to originate in the OTA because it  affects images in the FOC as well as the WFPC as demonstrated by the bottom two rows of Plate 2. It is also affecting the wavefront sensors. 
If the spherical aberration were introduced by a figure error on the secondary mirror, there would be coma with a linear dependence on field angle. There would be about 0.5 waves rms of coma at the FGS. and essentially no interferometer fringe visibility (S-curves) would be seen, contrary to observation. The FOC also does not exhibit significant coma. Hence, the major error is on the primary mirror. 
NASA appointed a commission chaired by Dr. Lew Allen to investigate the cause of the problem. The Allen commission has uncovered an error of 1.33 mm in the placement of a field lens in the reflective null corrector used in the manufacture of the HST primary mirror. This error alone would lead to the primary mirror having a conic constant consistent with  the value of -1.01324+- 0.00005  that they derive from ground test interferograms and would lead to an on-axis wavefront error in the OTA of 0.40 waves rms at 633 nm. Within the uncertainties this is consistent with the error of 0.43 waves derived from the on-orbit images.
Our understanding of the observatory performance is still at a preliminary stage in many respects. The optical problems are understood well enough to predict the effects on most  observations, yet not well enough to install corrective optics in future science instruments. The pointing system is fairly well characterized, but the effectiveness of flight software changes is still unclear. Finally, in areas such as sky background and baffling efficiency, UV throughput, target acquisition, internal optical alignments, and scattered light there are many unanswered questions.  We are now beginning the Science Verification (SV) period.  Most of these questions should be answered by the end of SV.
NASA presently plans to replace the WFPC with a 'clone' instrument fitted with corrective optics. The idea is to reimage the pupil onto the secondary mirrors in the camera repeaters by adding power to the folding flats after the pyramid in the PC. In the WFC the pupil is already close to the secondary. An exactly compensating amount of spherical aberration is then added in each of the eight camera secondaries, and should then give achromatic correction over the full Wide field and planetary camera fields with no extra reflections. There are several technical issues that must be resolved in order to successfully proceed with this program.
It is important to maintain the focal ratios of the cameras. As the folding flat will have power in the PC, the secondary mirrors will need to be changed in radius to compensate, and the camera despaced accordingly to achieve the correct focus. We do not regard this as a technical obstacle, but it does represent a departure from the baselined clone design as we understand it.  If the camera focal ratio is changed (from F/30 to F/28), the main disadvantage would be a need to modify many documents,  recode large amounts of software, and modify several databases. We would also lose the simple factor of 2 relationship of the FOC and PC pixel  sizes.
A more serious objection concerns the pointing. An optimistic scenario is that we achieve  reliable lock on 13.5 magnittude stars (presently, we have an operational constraint at 13th), that the proportion of binaries is 10% (prelaunch, the proportion of unflagged binaries in the GSC that were expected to fail to lock due to duplicity was 20% ; On orbit data indicates that 10% may be a better estimate, but the guide stars were preselected by other means in certain cases), that the spacecraft roll can be chosen freely (This seems unlikely because of a need to avoid the sun/moon/earth on faint objects, terminator constraints and possible target position angle requirements), and that the star density does not vary  significantly at galactic latitudes exceeding 30 degrees. Then there is a 30 percent loss of sky away from the galactic plane to fine lock. In reality the proportion is likely to be significantly higher.  It is therefore crucial that coarse track be improved and fine lock on only one guide star be implemented. (with coarse track to control the spacecraft roll)
Some science programs that were planned with the WFPC  will not be feasible with the clone. For example, any program that uses the pyramid to occult a bright object and examines its environs in a different camera for faint objects will be in trouble, because the aberrated light from the bright source is introduced into that camera. 
The coalignment of the four fields  with the Baum spots will be more demmanding because their images will be aberrated.
Bright sources are extended on the pyramid, and may scatter at pyramid pinhole defects, or dust contamination sites. The scattered light might then produce an aberrated ghost image on the detector.
There are indications that the beam in the WFPC repeaters is misaligned by perhaps 15%  on the secondary mirrors in the cameras. Further, bright star images may indicate a rotational misalignment of a few degrees of the camera spider images  relative to the OTA spiders. .Thus at the existing cameraheads there is probably enough misalignemnt that unacceptable coma would be introduced if a spherical aberration fix were applied there.  The beams in the cameras each need to be aligned to about 1% accuracy. This corresponds to a decenter of about 60 microns, or a tilt about the HST focal plane of about 1.5 arcminutes, or 0.5mm over a 1m baseline. It will be extremely demmanding, if it is possible at all to position the optics to these tolerances on orbit. It is not clear that the latch positions are known to that accuracy, and the internal alignments are more demanding. Any reflective element halves the tilt tolerance 
Preliminary evidence suggests small focus changes at least in the WFPC images on the timescale of a few orbits. They are equivalent to 5 microns OTA secondary mirror despace changes, and correspond to the outer rings in the image increasing by about 5% in diameter. If these effects are internal to the cameras then they may indicate a time dependence in the internal alignments. 
The effects of these misalignments and possible time dependences might have been noticeable in a nominal  HST, but they could destroy the possibility of correcting the clone.
The pointing performance is also degraded, with guide stars for fine lock presently limited to 13th magnitude, compared to an expected limit of 14.5 magnitude. Some areas of the sky are therefore not accessible in fine lock.  In addition, the spacecraft undergoes severe pointing disturbances during portions of the orbit, caused by thermal shocks.  
Coarse track is strongly dependent on magnitude and is worse than the predicted 21 milliarcseconds because of the image spread induced by the spherical aberration.  In fine lock, tracking is essentially within specifications during quiescent periods, and is almost magnitude independent.  However, fine lock cannot be reliably obtained with the full pupil; This is probably explained by aberrations in the system because of still imperfect alignment of the telescope, or secondary effects of the spherical aberration in the FGS optics. In theory, the interferometric system used in  fine lock is unaffected by symmetric aberrations (such as focus and spherical) but the large spherical aberration of the telescope could generate some coma and astigmatism terms within the FGS optics because of misalignments. 
In order to reliably obtain fine lock, use of the 2/3 aperture pupil stop is mandatory  which presently limits fine lock to stars brighter than 13th magnitude. An active program is under way to  improve the guiding capability.  It is hoped that tuning of system parameters, and perhaps changing  the telescope collimation will allow operation in fine lock at the predicted limit of 13.5 magniutude with the 2/3 aperture stop, and also improve coarse track.
Each FGS has a field consisting of an annular quadrant of the OTA focal plane between 10.2 and 14 arcminutes off axis. The HST guiding system had been designed to operate on stars of 14.5 magnitude  to give  an 85% probability of finding guide stars at high  galactic latitude.  The effect of limiting the guide stars to 13.5 magnitude as opposed to 14.5 magnitude is less severe for the axial instruments than for the WFPC, which does not benefit significantly in sky area for candidate guide stars when the spacecraft is rolled about the target in the aperture.  Hence in the absence of other scheduling constraints, the impact on the axial instruments is relatively small , while sky coverage in fine lock for the WFPC is reduced to 70% for galactic latitudes greater than 30 degrees if only one pair of guide stars is needed or 25% if two pairs are required in order to give protection against failure to achieve fine lock because of duplicity.
As indicated in the previous section, it is difficult to theoretically predict the PSF as a function of field position for deconvolution purposes.  On the other hand, direct reference observations of the PSF  will usually suffer from different jitter to the target  data. In any given image, the observed  PSF is the convolution of the instantaneous PSF from the last section with a jitter blurring function. This function is observed by the FGS and gyros, and might be determined from engineering telemetry.
An unrelated problem of the current guiding performance is the strong jitter and loss of lock induced by the day/night transitions. For 2 to 3 minutes associated with  passage from orbital day to orbital night or vice versa, thermal shocks in the solar arrays create line of sight jitter with 150 milliarcsec peak to peak amplitude and components of 10 and  2 second periods. Smaller oscillations (15-30 milliarcseconds) occur intermittently during the remainder of the orbit . The points in Figure 4 exclude such disturbances.  The oscillations cannot currently be compensated by the pointing control system,and the day night transitions almost always produce loss of fine lock, although coarse track with its larger dynamic range is maintained.
e of still imperfect alignment of the telescope, or secondary effects of the spherical aberration in the FGS optics. In theory, the interferometric system used in  fine lock is unaffected by symmetric aberrations (such as focus and spherical) but the large spherical aberration of the telescope could generate some coma and astigmatism terms within the FGS optics because of misalignments. 
