Image recovery at a resolution limited only by diffraction is now possible at large telescopes. The theory of speckle image reconstruction is explained and the current status of a video recording and digitization system for the reconstruction procedure is described. Potential applications of the process when used with very large telescopes are discussed. The constraints on telescope design imposed by these techniques are listed

Hewitt, A.

Nisenson, P.

Papaliolios, C.

Stachnik, R.

English

NASA Technical Reports Server

  
 
 
N O T I C E 
 
THIS DOCUMENT HAS BEEN REPRODUCED FROM 
MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT 
CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED 
IN THE INTEREST OF MAKING AVAILABLE AS MUCH 
INFORMATION AS POSSIBLE 
https://ntrs.nasa.gov/search.jsp?R=19800020716 2020-03-11T18:01:42+00:00Z
t
R
(NASA-CR-163393) NIGH RMIMION IMAGING AT 	 M80-29217
LARGE TELESCOPES (Harvard Univ.) 18 p
CSCL 03A Uncl as
:3/89 26389
KITT PEAK NATIONAL OBSERVATORY CONFERENCE
OPTICAL AND INFRARED,
TELESCOPES FOR THE 1990s
TUCSON, ARIZONA
7-12 JANUARY 1980
PROCEEDINGS
VOLUME T
EDITED BY
ADELAIDE HEWITT
MAY 1980
KITT PEAK NATIONAL OBSERVATORY, TUCSON, ARIZONA
a
-401-
HIGH RESOLUTION IMAGING AT LARGE TELESCOPES
P. Nisenson, R. Stachnik, C. Papaliolios
Harvard University
Cambridge, MA 02138
ABSTRACT
Image recovery at a resolution limited only by diffraction is now
possible at large telescopes. We give a brief review of one approach
to high resolution imaging and cite recent results to give the reader
an appreciation of its current state of development. We also summarise
potential applications of the process when used with very large tele-
scopes and list the constraints on telescope design imposed by these
techniques.
1. THEORY OF SPECKLE IMAGE RECONSTRUCTION
Speckle imaging is derived from speckle interferometry. In both
cases the input data consist of large numbers of images recorded with
the exposure times short enough to "freeze" the atmospheric blur. In
speckle interferometry, spatial power spectra of the individual images
are summed directly and the result is a power spectrum whose higher
spatial frequency components, out to the diffraction limit, character-
ize, not the atmosphere or telescope aberrations, but the source.
This technique is well known and has been extensively demonstrated.)
Power spectrum analysis does not allow recovery of true images, however.
,i
ii
4
-402-
Several procedures have been devised to permit full image recovery.'' '"
in the one we describe here, based on a technique first suggested by
Knox and Thompson, s
 the objective of obtaining a diffraction-limited
Fourier transform of the source, which can then be inverted to give an
image, is naturally separated into two problems: finding the amplitude
and finding the phase of the transform.
In this process, each image, I(x), is fourier transformed (t(G)))
and the ensemble average of four separate quantities is performed:
< t(w)> _ < a(w) ez(u) >	 (l)
< It (W+) I 2 > _ < ja(w) 12 >	 (2)
< t * (w) f (w + AWX) >
i (O (w + AW ) - (w)
_ < a(w)a(w + Awx) e	 x	 >	 (3)
< t*(W'A (W + &J >
i (O (W + AW ) - ^ (W) )
_ < a(w)a(w + Aw) e	 y	 >	 (4)
where
t(w) = 1 I(x)e Zwx di , and < > is the expected value.
i
In the first quantity, the effects of image shifts are removed
from the fourier transform phase before ensemble averaging. This
yields the recentered direct sum which is used both for reweighting
the low frequencies in reconstruction and for estimating the biases in-
troduced by photon noise.
The second quantity is the standard speckle power spectrum, from
which the recon: truction amplitudes are obtained.
The third and fourth quantities are used to save and ensemble aver-
age the transform phases. AWE and A 
y 
may be arbitrarily chosen to be
i
-403-
small anough so the phases in each realization of quantities (3) and
(4) never exceed n (or ± 7f/2). This avoids 2n ambiguities during the
ensemble averaging and allows the phase errors introduced by atmospher-
ic aberrations to average to zero. After averaging, the "phase differ-
ences" obtained in this way must be reintegrated to obtain the recon-
struction phases, and since there is always residual noise after aver-
aging, we have found it useful to use an iterative least squares fit-
ting technique such as that developed for active optical systems.6
This approach uses the redundancy in the Fourier transform to average
out errors in any given phase path. The phases thus derived are then
combined with the reweighted amplitudes, obtained from quantities (1)
and (2), to produce the reconstruction fourier transform, which is
finally retransformed to obtain an image. A flow diagram of the en-
tire process is shown in Figure 1. The bias subtraction operation re-
fers to compensation for photon noise and only applies in the low light
level regime.
2. CURRENT STATUS
Our recent work has concentrated on algorithm testing, processing
of actual data, and development and testing of a video recording and
digitization system.
Laboratory tests have successfully demonstrated the aberration
insensitivity of the process and its usefulness at low light levels.
Figure 2 is a demonstration of the reconstruction procedure at a
relatively high light level. 2a-b show the input test object, the
i••404-
W
4
i
Z0
U
HN70
W W
cr a	 HW^
w
Q
W
JYUW
CL
cn
0W
^
Z ^
•'^7W
2^ OV W
W
-405-
Greek letter gams and a point and the diffraction-limited image, re-
spectively. 2c in an image of an unresolved 6th magnitude star taken
on film at the 2.1-meter Kitt Peak telescope, and 2d is the result of
convolving 2c with the test object. 2d is formally equivalent to a
single speckle frame taken at the telescope. 2e is the direct sum of
100 such frames, and 2f is the 100 frame reconstruction obtained from
speckle processing. The recovered image is quite similar to 2b, the
aberration-free diffraction-limited image.
Other results, to be published elsewhere, include reconstruction
of the 0.05 arc-second separation binary star Capella, from data taken
at the 5-meter Palomar telescope, recovery of an improved resolution
image of a complex solar feature from images taken at the 0.75-meter
Sacramento Peak telescope, and diffraction-limited reconstruction of
binary stars from speckle data taken with a laboratory device simulat-
ing telescope aberration and atmospheric turbulence.
All of the data described in the foregoing were recorded on film
and digitized with the aid of a microdensitometer. Electronic record-
ing and real time digitization and processing have obvious advantages.
Eventually, particularly with array processing, on-telescope data re-
duction should be a straightforward matter. At present, we and others,
perform the reconstruction process only with data returned to the labo-
ratory, although on-telescope speckle interferometry has been demon-
strated by several groups.
In our approach, an effort was made to keep the field equipment
extremely simple, light and reliable. An ISIT video camera, operating
at 60 fields per second, and a video-tape recorder are used at the
N
d
W
-406-
It
-407-
telescope, and the data are digitized and recorded on a 9-track tape
in the laboratory for subsequent processing. A shutter exposes l
field in 8 (although the erase beam operates for 7 fields out of 8)
and a light source is used to saturate the target between exposures.
Both precautions are taken to insure complete erasure of the silicon
surface between exposures. The particular choice of 1 field in 8 for
exposure was set by the rate at which at 125 i.p.s., 1600 b.p.i. tape
drive will accept (128) 2 8-bit digitized images. A tone on the audio
track marks expused frames for the laboratory digitizer. Figure 3 in-
cludes schematic diagrams of the camera and digitizer.
A very brief discussion of the low light level case is in order,
at this point, because of the number of interesting objects at that
light level and because it is in this regime that a very large tele-
scope may be expected to make important contributions.
The individual frames upon which one operates are affected by pho-
ton noise even for relatively bright sources. This is the case because
exposures are short (N 0.01 second), spectral bardpasses must be re--
stricted (for a 25-meter aperture, AX ^ 4 am), and magnifications are
high (typically, at very large telescopes, hundreds of resolutions
elements are required across the seeing disk). At the 5-meter Palomar
telescope, one records only 100 photons per frame for a 10th magnitude
source. Furthermore, the relevant parameter for determining rate of
convergence is not the integrated sc- ,arce brightness, but surface bright-
ness. A 10th magnitude 1 arc-second source will require many more
frames for convergence than a 10th magnitude 0.2 arc-second source.
Analysis shows that the introduction of photon noise leads to the
presence of phase and amplitude bias terms in the reconstruction fourier
-408
A
OF t'tN )tl fir ' 1t.T t'Y
N
s
WO
O
r
w
bi
bs~10, W mJ ^^ •^JJ It}^ C
J O
CLV
r
W
Kt
12	
4
u^
a p
u	 41
:C 'N UJ
ut
vi -7u.
Q.
90
J
Si
00
.^.	 0 0 0
0 C
r,
d
v
jr
ai& w
-409-
transform. Images recovered from such transforms sre severely degrad-
ed. However, it is possible to deduce the bias terms from the Courier
transform of the direct sum of the images (Eq. 1) and to compensate for
the influence of photon noise. A demonstration showing experimental
verification of this fact is reproduced as Fig. 4.
4a is a double Gaussian test object. 0 is the Same double Gaus-
sian convolved with an actual film-recorded 2.1-meter telescope point
spread function (unresolved star speckle image) and poisson-distribut-
ed photon noise to simulate an object with 3 x 10 3 photons per frame.
4c is a reconstruction attempted without noise bias compensation, and
4d inclu4es bias compensation. The bias parameters were derived from
the direct sum transform.
This figure demonstrates that photon bias compensation is neces-
sary and that it can be quite successfully implemented. It should be
noted that at very low light levels both the data recording and process-
ing constraints may be considerably relaxed. Recording bandwidths be-
come smaller and innovative photon position-cataloging detectors may
be used in place of devices which record large 2-D arrays that are
mostly null. Processing is simplified by the fact that one deals with
correlations of small numbers of events rather than with complex,
large-array, 2-D Fourier transforms. Problems of low light level detec-
tion. and processing are actively being investigated.
Al
.49 A
10
tr	 r	 .^;
	
w	 ^• r }
W
S
r
{ ilr ti,.
. LARGE TELESCOPE CONSIDERATIONS
The telescope design requirements set by speckle imaging are iden-
tical to those appropriate to any of the high resolution image recon-
struction techniques known to us, and are most easily understood in
terms of the data taking constraints.
The data consist of direct images having;
e Exposure timos short enough to freeze atmosphere-associ-
ated image structure changes (ti 0.1 to 0.01 second):
• Limited spectral bandpass, so that the diffraction-limited
speckles (int:,k.erence fringes) are sharp over the
seeing disk of an unresolved stag;
• Ade=quate intensification and magnification to record the
diffraction-limited structure=
• No object structure change during they record sequence.
Only the first and second requirements have implications for tele-
scope design. The exposure time requirement suggests that high fre-
quency vibrations moving the telescope through more than a diffraction
spot width (0.005 arc-second at a 25-meter telescopes) must not occur
on a time scale shorter than that set by the atmosphere change time.
Note that there is no strict requirement on guiding accuracy, only
that individual exposures not be blurred.
The second requirement, on bandpass, implies an obvious assump-
tions that adequate coherence is present to insure that speckles are
visible at all. At a given telescope, in 1 arc-second seeing, the
second requirement is met if the bandpass is held to approximately
2XI0, where X is the wavelength of observation and Z0 is the
-412-..
diffraction resolution limit in arc-soconds. At a hypothetical 25-
meter telescope, the requisite bandpass is 4 nm. A 4 nm bandpass im-
plies that the telescope-induced wavefronL•
 error may approach 50-100
waves before coherence loss becomes very serious. It has already been
demonstrated that high resolution image recovery is possible as long
as the telescope aberrations are small anough to allow resolution of
the seeing disk.
While we have yet to experimentally verify the number of frames
of data required to assure convergence to a diffraction- limited
 recon-
struction characterized by a particular signal-to-noise ratio, we do
have analytical estimates substantiated by our digital simulation.
These indicate that a 6th magnitude, 1 arc- second source, observed at
a 2-meter telescope, will converge in 400 frames. This number scales
with the inverse square of the number of photons per resolution patch,
a number which can be computed for different telescopes, source sur-
face brightnesses and patch sizes. It should be noted that, by opting
for a resolution lower than the diffraction Limit, one can greatly re-
duce the number of frames required.
At very large telescopes, the full diffraction-limited resolution
can be achieved at an acceptable signal-to-noise in a reasonable num-
bar of frames only for high surface brightness objects. Even such
relatively high surface brightness objects as the outer planets require
a sufficiently large number of fr..mes for diffraction-limited resolu-
tion that rotational blurring becomes a problem. For planetsry sources,
one is forced to accept a lower recovered resolution; nevertheless,
for a typical object, Titan, the scaling law indicates rotation-limited
,resolution at a 25-meter telescope would be about half the diffraction-
J
.i
F_.
-413-
limited resolution. This is still very high resolution. Synoptic ob-
servations of planetary meteorology will be possible at resolutions
exceeding that of the space telescope. Even for the Pluto, the resolu-
tion will be 0.02 arc-seconds.
Surface features, if any, on stars of large angular extent will
be quite readily observable because of the very high surface brightness
of the sources. Figure 5 shows the result of plotting a selection of
the 100 brightest stars on a color magnitude diagram together with
lines of constant angular, diameter determined from an expression given
by Warner. 7 The figure demonstrates that while a relatively small num-
ber of stars are resolvable at the 5-meter, many more are open to
study at a larger telescope. At a 25-meter, about 300 resolution ele-
ments are present over the surface of the star Mira. Many more candi-
date stars would appear on Figure 5 if the list were extended beyond
the 100 bri.-!htest.
In a list due to McAllister, 9 it is estimated that N 250 binary
stars with spectroscopically-determined orbits would be resolvable at
a 25-meter, telescope. Combination of the visual orbit with spectro-
scopic elements would double or triple the number of stars on the mass-
luminosity diagram and extend it to include stars from 09 to M2. 13
supergiant masses would be measurable. Perturbations in pre;;isely
determined binary star orbits could also be used to reveal the pres-
once of low-mass, non-luminous components.
Image reconstruction of circ:unstellar shells, quasars, seyfer ga-
lactic nuclei and expanding nova shells (which, combined with spectro-
scopy, give distances) are also possible.
1-414-
5METIwR
TELESCOPE
,a Con
aBoo
eaAur
STARS RESOLVABLE AT 5 AND 25
METER TELESCOPES
(FROM LIST OF 100 BRIGHTEST,
ALLEN, 1964)
00100
00 Sco1, a Tcu25 ME1 ER ,iQGem
TELESCOPE yC"u
aUMa	 aAri,	 aTra
2	 8Ccn	 Car	 . OCet RAnd/3CEt..
	
, U allya.
EEoo phe Cos%ESw ^YA nd ^UM^;rU. Or&XVelso
rvCyg 04 Cet	 E Peg Y •Q Peg
3
V
4	 .XAyr
•BAyr
INCREASING
ANGULAR
log d"=0.73 (B-V)•O.2V-2.512	 DIAMETER
WARNER, MNRAS, 158, IP.
.8	 1.0	 1.2
	 14	 1.6
	 1.8
	 2.0
	 2.2
8-V
Figure 5
.J
4-415-
The success of high angular resolution interferometry and imaging
techniques gives added justification for the construction of telescopes
of greatly increased aperture size. For certain classes of objects,
angular resolution could be obtained well beyond that projected for
space telescopes of the foreseeable future. The principal telescope
design constraint imposed by these techniques is optical system coher-
ence to within, perhaps, 50 wavelengths in the visible.
ACKNOWLEDGEMENT
We gratefully acknowledge the interest and support of Richard
Goody, Robert Noyes, and Jerome Apt, and express our thanks to Paul
Horowitz for his design and construction of the video digitizer. This
work was carried out with NASA and Air Force support under Grants
NGL-22-007-228, and F19628-78-C-0026, respectively.
-416-
FIGURES
1. Flow chart outlining the speckle image reconstruction process.
Details are given in the text.
2. (a) is an input test object, a gvma and a point.	 (b) is the test
object filtered to have the ,Zpp ,.­ - ance of a telescope diffraction-
limited image.	 (c) is an actual 2-meter telescope point spread
function (stellar image), which, in (d), is convolved with (a) to
produce an image degraded in a highly realistic way by atmospheric
seeing.	 (e) is a direct sum of 100 realizations like (d) and (e)
is the image reconstructed from the same 100 frames.
3. Schematic diagrams of the on-telescope video image recording sys-
tem and laboratory-based video-tape data digitizer.
4. A demonstration of the photon-noise bias subtraction procedure
described in the text.
5. A color magnitude diagram on which are plotted a selection of ob-
jects from a list of 100 brightest stars as well as curves of con-
stant .angular diameter for diameters equal to the diffraction
resolution limit of 5-meter and 25-meter telescopes.
i
A
4
9
--417-
1. See, for example, Labeyrie, A., 1978, Ann. Rev. Astr. Ap., 16, 77.
2. Nisenson, P., and Stachnik, R. V., 1979, in Proc. I.A.U. Col. #50,
eds. J. Davis, W. J. Tango (Sydney: Chatterton Astronomy Dept.,
r
Univ. of Sydney), 34-1.
3. Fienup, J. R., 1978, Optics Letters, 3, 27.
4. Brown, T. M., 1978, J.O.S.A., 68 0 883.
5. Knox, K. T., and Thompson, B. J., 1974 0 Ap. J., 193, L45.
6„ Hardy, J. W., L,efebure, J. E., and Kolipoulos, C. L., 1977,
[	
J.O.S.A., 67 0 360.
f	 7. Warner, B., 1972 0 M.N.R.A.S., 158, 1p.
S. McAllister, H. A., 1980, private communication.
. 'j


High resolution imaging at large telescopes

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server