Matt Bolcar's Research Page
As future science missions call for larger and larger aperture space
telescopes, we see the technology begin to move toward one of two trends:
segmented apertures and multilple aperture telescopes. In either case,
the light from each segment or sub-aperture is combined to form an image
or fringes in the detector plane. The resulting resolution is comparable
to a monolithic aperture of size equal to the extent of the segments or
Fig. 1 - The James Webb Space Telescope, a segmented aperture system.
Fig. 2 - The Terrestrial Planet Finder - Interferometer, a multiple aperture
In order for the combination to occur, the segments or sub-apertures
must be "phased" - that is, the optical path length for rays
striking each segment, or passing through each sub-aperture must be equal.
The excessive size of these systems and the remoteness of their orbit
prohibits the use of interferometers to perform the phasing. Therefore,
image-based wavefront sensing techniques such as phase retrieval and phase
diversity have been identified as enabling technologies for future space
My research is to test and expand the ability of phase retrieval and
phase diversity techniques for such systems. For example, conventional
phase diversity is performed by capturing multiple images with the system,
each differing by a known defocus error. One technique I considered is
to use the already existing optical hardware of segmented and multi-aperture
systems to create the phase diversity by introducing known path-length
errors in a subset of the segments or sub-apertures. We found that this
technique works approximately as well as conventional focus diversity,
however without the need for extra hardware or detector planes to create
the phase diversity.
Fig. 3 - Conventional phase diversity is performed by collecting one or
more out-of-focus images in addition to the in-focus image.
Fig. 4 - Sub-aperture piston phase diversity is performed by adding a
known optical path-length error to one of the sub-apertures of a multiple
aperture system, effectively introducing a piston error over a portion
of the pupil function.
Another project has been to explore methods of multi-field wavefront
sensing for large systems. Typically, telescopes such as the Hubble Space
Telescope (HST) or the James Webb Space Telescope (JWST) have multiple
science instruments in the image plane, each occupying a portion of the
field of view. Traditional methods of wavefront sensing use only a single,
on-axis point source as the beacon for wavefront sensing. These methods
leave many field-dependent aberrations unsensed, and unaccounted for in
wavefront correction and image processing.
My project compared two methods of peforming the multi-field wavefront
sensing: one in which the field dependent aberrations were directly estimated
during the phase retrieval process, and one in which they were indirectly
calculated after processing phase retrieval results. We found that, in practice,
the direct sensing method showed an advantage in estimating the aberrations
of the system. This advantage became more apparent as the signal-to-noise
ratio (SNR) of the system decreased.
One of the tools used to evaluate these different methods and techniques
is that of Cramer-Rao bounds. Cramer-Rao bounds (CRBs) are an information
theoretic quantity that put a lower bound on the ability to estimate a
signal from a noisy system. An advantage of the CRBs is that they do not
depend at all on the estimation process, but only on the statistics of
the noise in the system and the system itself. The CRBs, therefore, provide
a "lowest common denominator" with which various algorithms
and techniques can be compared. The Cramer-Rao bounds are related to Fisher
In addition to these projects, I support the Wavefront Sensing &
Control group at NASA Goddard Space Flight Center under the direction
of Bruce Dean as part of my Graduate Student Research Program (GSRP) Fellowship.
The support consists of algorithm development and data processing for
various projects related to the James Webb Space Telescope.