tl;dr: It is not yet 100% clear to me what all of the optical tradeoffs are between on-axis and off-axis TMA's (see below), but part of the reason could be... politics? Note that I did find one reference to an off-axis telescope in space (see below):
...the Landsat data continuity mission/operational land imager (LDCM/OLI) instrument is an unobscured, wide field of view four mirror system, and has been reported as having no problems or delays during fabrication and alignment
See also
From Wikipedia's Nancy Grace Roman Space Telescope; Funding history and status:
Development of mission
The original design of Roman, called WFIRST Design Reference Mission 1, was studied in 2011–2012, featuring a 1.3 m (4.3 ft) diameter unobstructed three-mirror anastigmat telescope.13 It contained a single instrument, a visible to near-infrared imager/slitless prism spectrometer.
In 2012, another possibility emerged: NASA could use a second-hand National Reconnaissance Office (NRO) telescope made by Harris Corporation to accomplish a mission like the one planned for Roman. NRO offered to donate two telescopes, the same size as the Hubble Space Telescope but with a shorter focal length and hence a wider field of view.14 This provided important political momentum to the project, even though the telescope represents only a modest fraction of the cost of the mission and the boundary conditions from the NRO design may push the total cost over that of a fresh design.
13Green et al. (2012)Wide-Field InfraRed Survey Telescope (WFIRST) Final Report
14New York Times (June 4, 2012) Ex-Spy Telescope May Get New Identity as a Space Investigator (paywalled sometimes?)
What (the heck) is a Three Mirror Anastigmat?
For a narrow field of view, like when we look at a planet through a telescope of focus light from one object on the slit of a spectrograph, a normal on-axis telescope design is fine.
So that's how Hubble works, it's a standard Ritchey–Chrétien telescope:
A Ritchey–Chrétien telescope (RCT or simply RC) is a specialized variant of the Cassegrain telescope that has a hyperbolic primary mirror and a hyperbolic secondary mirror designed to eliminate off-axis optical errors (coma). The RCT has a wider field of view free of optical errors compared to a more traditional reflecting telescope configuration. Since the mid 20th century, a majority of large professional research telescopes have been Ritchey–Chrétien configurations; some well-known examples are the Hubble Space Telescope, the Keck telescopes and the ESO Very Large Telescope.
Apparently this design is now "old and busted" and the Three Mirror Anastigmat is the "new hotness".
A three-mirror anastigmat is an anastigmat telescope built with three curved mirrors, enabling it to minimize all three main optical aberrations – spherical aberration, coma, and astigmatism. This is primarily used to enable wide fields of view, much larger than possible with telescopes with just one or two curved surfaces.
A telescope with only one curved mirror, such as a Newtonian telescope, will always have aberrations. If the mirror is spherical, it will suffer from spherical aberration. If the mirror is made parabolic, to correct the spherical aberration, then it must necessarily suffer from coma and off-axis astigmatism. With two curved mirrors, such as the Ritchey–Chrétien telescope, coma can be minimized as well. This allows a larger useful field of view, and the remaining astigmatism is symmetrical around the distorted objects, allowing astrometry across the wide field of view. However, the astigmatism can be reduced by including a third curved optical element. When this element is a mirror, the result is a three-mirror anastigmat. In practice, the design may also include any number of flat fold mirrors, used to bend the optical path into more convenient configurations.
These come in both on-axis and off-axis flavors!
On-axis Three Mirror Anastigmat
The light path and mirrors of a Paul-Baker telescope, an example of a three-mirror anastigmat. https://www.ast.cam.ac.uk/about/three-mirror.telescope
Source
From Three Mirror Anastigmat:
Examples
- The James Webb Space Telescope is a three-mirror anastigmat featuring an ellipsoidal primary, hyperboloidal secondary, and ellipsoidal tertiary.6
- The Euclid mission will use a Korsch telescope.
- The "Cambridge University Three-Mirror Telescope". project includes a 100 mm working model built in 1985 and a 500 mm prototype built in 1986.
- The Vera C. Rubin Observatory's telescope (formerly known as Large Synoptic Survey Telescope) is a modified three-mirror anastigmat of Paul–Baker design.
- The KH-11 Kennen (or perhaps the now cancelled Future Imagery Architecture) telescopes may be a three-mirror anastigmat, since the spare telescopes given to NASA by the National Reconnaissance Office are of this form.
- The Extremely Large Telescope will be a three-mirror anastigmat design, with two additional flat fold mirrors.
- The Deimos‑2 and DubaiSat‑2 Earth observation satellites both carry a three-mirror anastigmat Korsch design telescope.7,8
- Ralph imaging spectrometer on New Horizons spacecraft
- The Nancy Grace Roman Space Telescope, formerly named the Wide Field Infrared Survey Telescope (WFIRST), employs a folded three-mirror anastigmat featuring an ellipsoidal primary, hyperboloidal secondary, and ellipsoidal tertiary.9 An earlier design used an off-axis three-mirror anastigmat.10
6"Optical design and analysis of the James Webb Space Telescope: optical telescope element" (paywalled)
7DEIMOS-2: cost-effective, very-high resolution multispectral imagery (paywalled conference proceedings) viewable abstract)
8"Technical Specifications of DubaiSat 2" (broken link)
9Optical design and predicted performance of the WFIRST phase-b imaging optics assembly and wide field instrument (paywalled, but readable at Researchgate and NASA NTRS)
10Optical Design Trade Study for the Wide Field Infrared Survey Telescope (WFIRST) (also readable in Researchgate)
And this is what the off-axis TMI would have looked like:
From the 2012 Optical Design Trade Study for the Wide Field Infrared Survey Telescope (WFIRST) before they accepted the existing on-axis spy telescope:
4.1 IDRM description
The major change from JDEM-Omega is the switch to an unobscured telescope form. The advantages of this form for dark energy science have been pointed out before (16-18) , but include improved MTF since the large central obscuration for stray light baffles (JDEM-Omega had a 50% linear obscuration) is not needed, improved sensitivity due to no loss of area, and increase in flexibility in design due to the aperture bias that more naturally allows beam clearance. One advantage of the uTMA over the three mirror system without an intermediate focus is the stray light reduction possible by the placement of a field stop at the intermediate focus, limiting stray light entering the instrument volume. Drawbacks of the unobscured form include larger overall telescope packaging volume, somewhat tighter alignment tolerances, and potentially more difficult mirror fabrication and alignment. We felt this last point is often overstated when improvements in mirror fabrication and alignment tooling are taken into account. For example, the Landsat data continuity mission/operational land imager (LDCM/OLI) instrument is an unobscured, wide field of view four mirror system, and has been reported as having no problems or delays during fabrication and alignment19
19OLI telescope post-alignment optical performance (paywalled)
What could have been (unobstructed aperture):
Figure 48: DRM2 payload optical ray trace
What is (six vanes plus central obstruction):
Figure 3-4: The telescope components without the outer barrel assembly.
Figure 3-5: The telescope entrance pupil
