atri 2
14
UEF // University of Eastern Finland UEF // University of Eastern Finland Under graduate seminar, 03/10/2016 Atri Halder LIMITS PROVIDED BY DIFFRACTION TO OPTICAL SYSTEMS AND PROBABLE WAY TO GET RID OF IT
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Transcript of atri 2
UEF // University of Eastern FinlandUEF // University of Eastern Finland
Under graduate seminar, 03/10/2016
Atri Halder
LIMITS PROVIDED BY DIFFRACTION TO OPTICAL SYSTEMS
AND PROBABLE WAY TO GET RID OF IT
UEF // University of Eastern Finland 03/10/2016Atri Halder 2
0th order
z
x
+ 1st order
- 1st order
Transmission function
Diffraction by a sinusoidal grating
T.F. = 1
21 + cos 𝑢𝑥
= 1
2+
1
4𝑒𝑖𝑢𝑥+
1
4𝑒−𝑖𝑢𝑥
15˚
UEF // University of Eastern Finland
0th order
+ 1st order
- 1st order
x
z
Transmission function
Diffraction by a sinusoidal grating
4
35˚
Atri Halder 03/10/2016
UEF // University of Eastern Finland 503/10/2016Atri Halder
0th order
x
+ 1st order
- 1st order
zDiffraction by a sinusoidal grating
-2nd order
+ 2nd order
UEF // University of Eastern Finland
Imaging by optical system
503/10/2016Atri Halder
L1
L2
Image plane intensity distribution
z
UEF // University of Eastern Finland
Diffraction pattern of a circuler aperture
3.10.2016Atri Halder 6
No
rmal
ized
in
ten
sity
X axis
Radious(R)
The diffraction pattern of a circular aperture is known as Airy Disc or Point Spread Function
UEF // University of Eastern Finland
Diffraction pattern of a circuler aperture
3.10.2016Atri Halder 7
U V
L
1. Focal Length2. Aperture3. Wavelength4. Source
UEF // University of Eastern Finland 3.10.2016Atri Halder 8
UEF // University of Eastern Finland 3.102016Atri Halder 9
UEF // University of Eastern Finland 3.10.2016Atri Halder 10
𝐿 = 1.22 𝜆
2 ݊ ߠ݊݅ݏ
UEF // University of Eastern Finland
Super-resolution
•Toraldo phase filter (The idea was first developed by G. Toraldo di Francia in 1947)
•Genetic algorithem or Particle swarm optimization
•Changing the shape of the Point Spread Function
3.10.2016Atri Halder 11
UEF // University of Eastern Finland
Synthesis of phase filters:
123.10.2016Atri Halder
Refference:
1) Joseph W. Goodman, Introduction to Fourier Optics, 2nd edition (McGraw-Hills Series).
2) Born, Max; Wolf, Emil (October 1999). Principles of Optics. Cambridge: Cambridge University Press. p. 461. ISBN 0-521-64222-1.
3) G. Toraldo di Francia, “Modern trends in the evaluation of optical images,” J. Opt. Soc. Am. 47, 507 (1957).
4) H. Hyv¨arinen, S. Rehman, J. Tervo, J. Turunen, and C. J. R. Sheppard, “Limitations of superoscillation filters in microscopy applications,” Opt. Lett. 37, 903–905 (2012).
3.10.2016Atri Halder 13
Thank you!
uef.fi
