1. 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

2. 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
2
1 + cos 𝑢𝑥
=
1
2
+
1
4
𝑒 𝑖𝑢𝑥
+
1
4
𝑒−𝑖𝑢𝑥
15˚

3. 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

4. UEF // University of Eastern Finland 503/10/2016Atri Halder
0th order
x
+ 1st order
- 1st order
z
Diffraction by a sinusoidal grating
-2nd order
+ 2nd order

5. UEF // University of Eastern Finland
Imaging by optical system
503/10/2016Atri Halder
L1
L2
Image plane intensity
distribution
z

6. UEF // University of Eastern Finland
Diffraction pattern of a circuler aperture
3.10.2016Atri Halder 6
Normalizedintensity
X axis
Radious(R)
The diffraction pattern
of a circular aperture is
known as Airy Disc or
Point Spread Function

7. UEF // University of Eastern Finland
Diffraction pattern of a circuler aperture
3.10.2016Atri Halder 7
U V
L
1. Focal Length
2. Aperture
3. Wavelength
4. Source

8. UEF // University of Eastern Finland 3.10.2016Atri Halder 8

9. UEF // University of Eastern Finland 3.102016Atri Halder 9

10. UEF // University of Eastern Finland 3.10.2016Atri Halder 10
𝐿 =
1.22 𝜆
2 ݊ ‫ߠ݊݅ݏ‬

11. 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

12. UEF // University of Eastern Finland
Synthesis of phase filters:
123.10.2016Atri Halder

13. 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

14. Thank you!
uef.fi