No, they don't need to have the same focal length "as if part of one single mirror" they just need to be capable of being phase aligned and close enough in FL that there's no detrimental effect on the image. They can be many wavelengths off in exact FL so long as the requirement for phase alignment is meant - which means they are adjusted physically so that the optical paths are the same length closely enough to allow phase coherence. Depth of focus of the individual segments accommodates this adjustment against absolute focal length, the more important factor is that the segments match in focal length so image scale isn't affected. What's important here is that the telescopes that do this are all under active control, with monitoring equipment (generally Shack-Hartmann sensors) to keep them aligned in use.
This paper on a 1/5th scale model of the GMT and the GMT design itself describes this, noting that rough positioning (to microns) is done with the segment's active support structures on a slow (0.01Hz) cycle, and rapid phase alignment will be done by a matching segmented active secondary... http://www.gmto.org/.../GMT_5494-8.pdf
Manufacturing the six off-axis segments is recognized as a challenge.
Most large mirrors have a loose tolerance on focus, equivalent to a tolerance on radius of curvature of 1 mm or more. The GMT segments have a much tighter tolerance on focus because of the need for all seven mirrors to have the same image magnification. The requirement is strictly that the segments must match in radius of curvature rather than that they all have the specified value. While we may be able to achieve better relative accuracy than absolute accuracy in radius, the fact that the mirrors will be made over a period of several years makes it more difficult to maintain a common standard. For the time being we are setting a goal of measuring the absolute radius of curvature to an accuracy such that each segment could be bent to the nominal radius with the active supports.
Alignment tolerances are relatively tight for the GMT because of the f/0.7 primary mirror. Optical alignment should be held to an accuracy that does not degrade image quality in any observing mode, from relatively simple groundlayer adaptive optics—correcting with only the deformable secondary mirror—to the most ambitious multi-conjugate or extreme adaptive optics whose goal is full diffraction-limited imaging. In all modes, the primary mirror segments must be positioned with sufficient resolution that residual alignment aberrations are a fraction of those caused by the atmosphere, and maintain this level over wavefront averaging intervals of about 1 minute. The aberrations will be measured in the wavefront and the immediate correction will be made with the adaptive secondary mirror, but the correction should not be allowed to be a large fraction of the correction needed for seeing.
We have analyzed the requirements for alignment of the GMT segments in the telescope. Rapid correction of all wavefront errors will be made with the adaptive secondary mirror, and slowly varying errors due to alignment will be transferred to the primary mirror segments. Tolerances for in-plane motion of the segments are loose compared with the resolution of the segments’ hard-point positioners.
Edited by mark cowan, 20 June 2016 - 06:17 PM.