ISSN 2394-3777 (Print)
ISSN 2394-3785 (Online)
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International Journal of Advanced Research Trends in Engineering and Technology (IJARTET)
Vol. 11, Issue 3, March 2024
All Rights Reserved © 2024 IJARTET 1
Concentric Zones With Different Amplitude Filters
Dr. A. Narsaiah,
Principal, ABV Govt Degree College, Janagaon 506167, Telangana.
B. Srinivasa Goud,
C. Assistant Professor of Physics ABV Government Degree College, Jangaon Telangana -506 167. India.
Dr.T. Kiran Kumar,
Assistant Professor, Department of Physics, Brilliant Institute of Engineering and Technology Hyderabad – 501505.
Abstract: In optical systems the apodisation technique employing aperture shading is implemented in three different ways.
The apodisation is affected over the entire pupil, The pupil is apodised over a limited zone and the pupil is divided into a
specified number of concentric annular zones, each varying in transmission from the other. The second kind of apodisation
is called the partial apodisation and the third kind is known as the variable apodisation which will form the subject matter
of this. All through the study optical systems with annular apertures apodised with the amplitude filters, namely Hanning
filter, Lancoz filter, Shaded aperture filter, Barlett filter and Butterworth filter of the first order have been considered.
Investigations have been made on the imaging properties of defocused optical systems suffering from primary spherical
aberration. The effects of variable apodisation on the diffracted field characteristics of apertures with Straubel class of pupil
functions. In their study, they have divided the pupil into different number of concentric annular zones.
Keywords: Aberration, Aperture, Hanning pupil and annular zones etc;
I. INTRODUCTION
General mathematical formulation for the
complex amplitude distribution in the defocused plane
of apodised optical system in the presence of spherical
aberrations has been presented. From the below
expression the expression for complex amplitude in the
case of variable apodisation with two filters when the
aperture is divided into two concentric zones can be
written as
rdr Zr J r
r
i r f Z G
s d s d F 0
4
2 5 . 0
4
1
2
exp 2 , ,
+
rdr Zr J r
r
i r f Z G
s d s d F 0
4
2 1
5 . 0
4
1
2
exp 2 , ,
Where f(r) is the amplitude filter. In the present study
the following filters are employed:
Expression gives the complex amplitude PSF of an
apodised optical system under the influence of defocus
and primary spherical aberration. The intensity or
irradiance PSF BF ( Z
s d
, , ) is given by the squared
modulus of the amplitude PSF. [5] discussed about a
review paper which brings out a summary of popular
image processing techniques in practice for students,
faculty members and researchers in medical image
processing field. Through Image processing, we do
some operations on an image, to get an enhanced
image or we try to acquire some useful information
from it.
1.2 MATHEMATICAL FORMULATION:
BF ( Z
s d
, , )= GF ( Z
s d
, , )
2
Accordingly the intensity PSF in the Gaussian focal
plane is given by,
BF ( Z
s
, , 0 )= GF ( Z
s
, , 0 )
2
In the defocused and aberration free plane the intensity
PSF is
BF ( Z
d
, 0 , )= GF ( Z
d
, 0 , )
2
For a clear aperture or for a perfect lens, f(r) = 1. The
expression for the normalized intensity at a specified
point in the Gaussian focal plane becomes,