Oct 3, 1988 - 92960, Worldway Postal Center, Los Angeles, CA 90009-2960. It was reviewed ... Oriented Investigation and Ezperimntation (NHOE) Program. ..... Aerophysics Laboratory: Launch vehicle and reentry fluid mechanics, heat.
P
A
REPORT SD-TR-88-95
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Optical System Defect Propagation in ABCD Systems/
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0 oW. CM
G. McKINLEY ITEK Optical Systems Lexington, MA 02173
I
H. T. YURA Electronics Research Laboratory The Uerospace Corporation El Segundo, CA 90245 and S. G. HANSON Riso National Laboratory DK-4000 Roskilde, Denmark
3 October 1988
Prepared for SPACE DIVISION AIR FORCE SYSTEMS COMMAND Los Angeles Air Force Base P.O. Box 92960 Los Angeles, CA 90009-2960
DTIC ELEC rE
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This report was submitted by The Aerospaoe Corporation, 1E 90245, imder Contract go.
.
-
Segundo,
.
CA
04701-85-C-0086 with the Spaoe Division, P.O. Box
92960, Worldway Postal Center, Los Angeles, CA 90009-2960. It was reviewed and approved for The Aerospace Corporation by N. J. Daugherty, Director, Electronics Research Laboratory. Lt Scitt LOvJasou,
SD/CNUD
.s the project officer for the Mission-
Oriented Investigation and Ezperimntation (NHOE) Program. This report has been reviewed by the Public Affairs Office (PAS) and is releasable to the National Teohnical Informtion Service (UTIS). At UTIS, it will be available to the general public, Including foreign nationals. This technical report has been reviewed and Is approved for publication. Publication of this report does not constitute Air Force approval of the report's findings or conclusions. It is published only for the exchange and stimulation of ideas.
HD!E Project Officer SD/CNID
rector, APSTC West Coast Office TC/CO
.
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REPORT DOCUMENTATION PAGE Im.IMPORT
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ORGANIZATION4 REPORT NUMUER5
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Th-0088( 925 -004)-2
SD-TR-88-95
Ga. NAME OFP ERFORMING ORGANIZATION
The Aerospace Corporation .Ahoratory Operations
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Space Division Angeles Air Force Base
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El Sepunio, CA 902415
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LOKUIT
r!"SSION no.
Optical System Defect Propagation in ADCD Systems 12. PERSONAL AUTHOR(S)
McKinley, W. G., Yurat H. T.9 and Hanson. S. G.
13a. TYPE OF REPORT
13b. TIME COVERED
14. DATE Of- REPORT (Vow, No
;;;Iy
S. PAGE COUNT
October 39
TO1988
FROM
16. SUPPLEMENTARY NOTATION
17. FIELD
COSATI CODlS GROUP SU4
II
I
10. SUIJECT TERMS (Con'u. an, ieWM if necounvy and Id&ntfy by bMock numibed 'ay decenters,
errors,
'~Despace
19. ABSTRACT (corfkwe on reveiie Nfneceua rad knbl
'
by block wusuber
This report describes how optical system defects (tilt/jitter, decenter, and despace) propagate through an arbitrary paraxial optical system that can be described by an ABCD ray transfer matrix. A pedagogical example is given that demonstrates the effect of alignment errors on a typical optical system./',,
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83 APR edition may be used until ehausted. All other editions or* obsolete.
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A general
methodology for analyzing beam wave propagation in complex
paraxial optical systems that can be described by an ABCD ray transfer matrix was put
forth
in
a recent publication (Ref.
1).
In the methodology
formalism for evaluating ray tilt in a general optical system. an addendum to Ref.
is
a
This report Is
1 which describes how additional optical system defects
may be included in the wave propagation analysis in a straightforward manner. First, the addition of ray decenters to the tilt analysis will be discussed. Second, the inclusion of despace errors will be discussed to complete the modeling of
alignment defects, and
lastly,
a
procedure for
modeling the
manufacturing errors of radius errors and cylinder errors will be identified. In Section 5 of Ref. 1 tilt and Jitter in optical systems were discussed and Eqs. (54)-(63) quantifying the description were presented.
Equation (54)
of Ref. 1 defines a Gaussian random tilt variable for the J-th optical element as
:-
ej
ZjI ,e 0
06
if a iIs generalized to include a Gaussian random displacement variable, then element decenters may also be modeled using the same formalism as outlined for tilts to evaluate ray decenters.
Generalizing Eq. (54) is straightforward:
by including a decentor error, hi, the tilt vector, now generalized, becomes
(h > -
