Introduction to aberrations

Transcription

1 Introduction to aberrations Lecture 8 Image and aberration evaluation 1

2 Aberrations and image: Aberration theory Aberration evaluation Image formation Image evaluation Geometrical and physical theories The image of a point object

3 Criteria The application determines the aberration tolerances Most usually the detector pixel size or the specification on resolution The case of visual instruments 3

4 Resolution Resolution is an important image quality metric It determines whether two closely spaced, and equal irradiance, objects can be identified as two mm Well resolved mm 5 Rayleigh resolution peak of nd at 1st zero of first 4

5 Resolution 5

6 Rules that rule optics RES k ; DOF k NA n NA 1 Wavelength=193nm k1~ Raleigh resolution k1=0.61 K~0.5 R(193 dry)=147nm (NA=0.8; k1=0.61) DOF=151 nm Must preserve imaging volume! Resolution and depth of focus are critical. R(193 water)=110 nm 6

7 Diffraction Encircled Energy in the Airy pattern % % 0.8 ENCIRCLED ENERGY st zero nd zero DIAMETER OF CIRCLE (MM) 7

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11 Aberration balancing 11

12 Wavefront variance in the presence of primary aberrations 1

13 Rayleigh-Strehl ratio 13

14 Rayleigh-Strehl ratio 14

15 Use of the central-ordinate theorem 15

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18 Andre Marechal formula I W I 1 1 W 18

19 Shack s formula I W I exp W 19

20 Shack s formula derivation 0

21 Shack s formula derivation cont. Given by an OPTI518 student 1

22 Rayleigh-Strehl ratio Rayleigh Strehl Aberrated PSF peak Unaberrated PSF peak See Lord Rayleigh, Investigations in optics, with special reference to the spectroscope, Phil. Mag. Vol. 5(8), , Strehl, K. 1895, Aplanatische und fehlerhafte Abbildung im Fernrohr, Zeitschrift für Instrumentenkunde 15 (Oct.), Strehl, K. 190, Über Luftschlieren und Zonenfehler, Zeitschrift für Instrumentenkunde, (July), V. N. Mahajan, Strehl ratio for primary aberrations in terms of their aberration variance, J. Opt. Soc. Am. Vol. 73(6) , 1983.

23 Rayleigh-Strehl ratio S ~1 w S ~ e w Approximation Good for S~>0.3 Good for S~>0.1 It is the variance of the wavefront deformation 3

24 Some Rayleigh-Strehl ratio insights Ratio of aberrated to unaberrated PSF peaks Scattered energy Contributions form refracting and reflecting surfaces Contributions from rough surfaces DOE efficiency Keep in mind formula limits S ~1 w 4

25 The case of refraction vs. reflection surface S ~1 1 n' n w n' n 0.5 refraction n' n 4 reflection Ratio of scattered energy is 16! Thus for a given surface roughness, reflection scatters 16 times more than refraction. Note dependence with wavelength 5

26 Marechal Criterion ~1947 Keep in mind that is not only the resolution but also the depth of focus. MUST PRESERVE ALL DOF!!! 6

27 Best focus according to variance W W

28 The concept of Diffraction limited Not limited by geometrical aberrations Depends on the particular technical field Usually means RSR > 0.8 A healthy human eye is diffraction limited at a pupil diameter of ~ 1.5 mm 8

29 Roland Shack s notes 9

30 Binocular quality Inexpensive binos Expensive binos 4X10 Double pass Double pass Spherical aberration in the eye: ~+4 waves for a 6 mm pupil at 587 nm. Or ¼ wave for a 3 mm pupil. 30

31 Topics Aberration/image evaluation Image of a point object Rules that rule the optics world Wavefront variance Aberration balancing Raleigh-Strehl ratio 31