The design and fabrication of holographic gratings requires an understanding of Fermat's principle. This principle states that the path of a light ray from one point to another is that which requires the least time. The aberrant, optical path of an object point to an image was studied using Fermat principles

Bhatia, M. S.

English

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https://ntrs.nasa.gov/search.jsp?R=19760011321 2020-03-22T17:07:49+00:00Z
rSEMI-ANNUAL STATUS REPORT
l
TO
THE NATIONAL AERONAUTICS AND SPACE AGENCY
FOR
HOLOGRAPHIC GRATINGS FOR SPECTROGRAPHIC APPLICATIONS:
STUDY OF ABERRATIONS
(Contract No. NGR21-027-010)
MANJIT S. BHATIA
PRINCIPAL INVESTIGATOR
BOWIE STATE COLLEGE
BOWIE, MARYLAND
(NASA-CE-146316)
	 HCLCGRAPHiC GRATINGS FOR
	
N76-18409
SPECTROGRAPHIC APPLICATIONS: STUDY OF
ABERRATIONS Semiannual Status Report (Bowie
State Ccll., Md.)	 7 F HC $3.50	 CSCL 14E	 Unclas
G3/35 18520
E:
Holographic Gratings For Spectrographic Applications:
Study of Aberrations
The design and fabrication of holographic gratings requires a
deep understanding of Fermat's principle. This principle states
that the path of a light ray from one point to another is that which
requires the least time. Utiliziug Fermat's principle, we study the
aberrant optical path of an object point A to an image point B (see
diagram below).
Y
A
We describe the aberrations (astigmatism, coma, spherical) of the image
point B of A by a difference between the optical path AM + MB and a
constant that is generally chosen equal to AI + IB; I being the origin
of the coordinate system. Then the aberrant optical path is:
A = (AM + MB) - (AI + IB) .
This symbolic equation represents a simplistic geometry for a conventional
grating. For a holographic grating, the above equation is written as
follows:
A = (MA + MB) - (IA + IB) - (MC - MD) - (IC - IA)	 = 0
0
i'•
J
A
Where the additional terms are the holographic grating terms. The
holographic contribution makes it possible to correct or reduce
aberrations such as astigmatism or coma as a function of wavelength.
The following diagram shows the use conditions and the recording ^(
conditions of a holographic grating.	 T	 1
A
X
Where: a0 = laser recording wavelength of radiation
C = recording point source
D = second recording point source
X = is the wavelength at image B of A.
K = is the order at which the holographic grating
operates (can be negative or positive).
A = point source under performance or use condi-
tions. At a specific angle a
B = the diffracted image under performance or use
conditions at some angle S.
For the past two and a half years we have gained a detailed knowledge
of the above brief presentation and have developed computer programs
which make it possible to design holographic reflecting diffiation
gratings useful in spectroscopic instrumentation. The programs are
C
f,
2
•~ t
capable of determining optimum design parameters (Y, 6, groove fre-
quency, K, rc , rd) as a fund.:.~ of use parameters (a, R, groove
{
frequency, K, ra , rb).
Where: a - angle between the normal to the grating and
the recording point C.
d = angle between the normal to the grating and
the recording point D.
r - distance from the center of the grating to
c	 the recording point source C.
= distance from the center of the grating tord
the recording point source D.
K = order in which the grating operates.
a = angle of incidence between the normal to the
grating and light source A.
B = diffracted image angle as a function of wave-
length between the normal to the grating and
the image B.
r - distance from the center of the grating to
a the light source A.
r  = distance from the center of the grating to the
diffracted image B.
Four computer programs have been developed to date. The first program
determines the optimum recording parameters for correcting astigmatism
and coma simultaneously at selected wavelengths for a Rowland circle
spectrographic mount. The program shows that solutions are possible
for correcting both astigmatism and coma at wavelengths equal to or
greater than the recording wavelength. The program then presents a
display of the numerical aberrations for both the conventional grating
and the holographic grating as a function of wavelength for any angle
3
of incident radiation. Normally, the display will be for the use
parameters for which the holographic grating was designed (a, S,
groove frequency, K, r a , rb ). The use of this program makes it
possible to design a spectrograph having the best conditions for
aberrations and optimum performance.
A second program was developed for a Rowland circle spectrographic
or monochromator mount to determine the optimum recording parameters
as a function of use parameters that corrects for astigmatism or
coma but not both simultaneously at selected wavelengths below, equal
to or greater than the laser recording wavelength. Solutions have
been or can be determined for all wavelengths. However, the program
shows that there is a trade off because when astigmatism is corrected
coma is greater and vice versa. Under certain conditions a happy
medium is achieved depending on the use parameters. This program
also displays the performance of the holographic grating and conventional
grating as a function of wavelength relative to numerical aberrations.
This program considers both negative and positive orders of the grating.
The third and fourth programs have been combined because one depends
upon the other. These programs determine optimum recording parameters
as a function of use parameters for fixed entrance and exit slits
relative to a grating rotating about its vertical axis. A literature
search shows that Greiner and Shaefer (2) and Namioka (3) have done a
considerable amount of work in this area. As a result, the third
program was developed to determine the optimum instrtmiental parameters
4
(rat rb , a, S, C, groove frequency) relative to a conventional grating.
C is the angle between the exit and entrance slits relative to the
grating. By coupling the information obtained from this program with
the holographic contribution, a fourth program was developed to
determine the optimum recording parameters required to design a
holographic grating. For a specified wavelength range, the combined
program for negative orders only, wi?.1 determine: the optimum use
instrumental parameters, and the optimum recording parameters for
either minimizing astigmatism or coma over a selected wavelength
range or it will correct astigmatism or coma at selected wavelengths
within the desired wavelength range. Then with this information
the computer program displays the performance of the conventional
and holographic gratings relative to the aberrations numerically.
The forgoing is a brief presentation of the work performed to date.
Detailed documentation of the computer programs are being prepared
and will be available in the very near fu;:ure.
For future work, a program will be developed with the grating opera-
ting in the posiLi-^,e order for an instrument utilizing a rotating
grating and fixed entrance and exit slits. We will also develop
computer programs for instruments using toroid type gratings because
they have the potential of improving the optical performance at
grazing angles of incidence.
5
REFERENCES
(1) G. Pieuchard, J. Flaman; Final report of Jobin et Yvon
to Goddard Space Flight Center, NASA (1972).
(2) H. Greiner and E. Shaffer; Optik 15, Issue 1 1958
(3) H. Noda, T. Namioka and M. Seya; J. Optical Society
of America, Vol. 64, No. 8 (1974)
.M
as


Holographic gratings for spectrographic applications: Study of aberrations

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