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Superresolving Phase Filters

Superresolving Phase Filters. J. McOrist, M. Sharma, C. Sheppard. Introduction. A lens brings light to a focus Geometric optics the focus is a point Physical optics the focus is a distribution of light known as a point spread function

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Superresolving Phase Filters

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  1. Superresolving Phase Filters J. McOrist, M. Sharma, C. Sheppard

  2. Introduction • A lens brings light to a focus • Geometric optics the focus is a point • Physical optics the focus is a distribution of light known as a point spread function • We can control the point spread function by changing the light at the aperture

  3. Back Focal Plane Front Focal Plane Basic Imaging System

  4. Focal Distributions • The point spread function has two components: - Transverse - Axial • Central peak is the central lobe, and the secondary peaks are the side lobes. • Resolving power is related to the size of the central lobe

  5. What is Superresolution? • Superresolution in general, is reducing the size of the central lobe below the classical Raleigh limit • Normally achieved by placing a filter in the back focal plane of the lens • While resolution is improved, the effectiveness is limited by: - the size of the side lobes (M) - Strehl Ratio - central lobe intensity (S)

  6. Superresolving PSF

  7. Problems and Motivation • Amplitude filters have two main problems: • Central lobe intensity • Fabrication of the filters • Little theoretical work in phase filters, in particular axial behaviour • Phase modulation is now possible with Diffractive Optics and Spatial Light Modulators

  8. No phase change Phase change of 0  Toraldo Phase Masks • Zone masks are very simple, both to produce and to analyse mathematically • This is the first type of mask we examined • Consists of two concentric zones • Sales and Morris first examined this type of Mask in the Axial Direction

  9. Theoretical Considerations • In the Fresnel Approximation we can describe the axial amplitude as1 • For a filter with two zones of equal area we get an intensity distribution 1. C.J.R. Sheppard, Z.S. Hegedus, J. Opt Soc. Am. A 5 (1988) 643.

  10. Theoretical Considerations • Due to its simple form we can easily determine the properties of the pupil filter • We determined values for the Strehl Ratio (S), Spot Size, and axial position. • We can also model the point spread function for values of 0

  11. PSF of Two zone Filter The PSF of two-zone mask as the phase varies from 0 to Pi

  12. Axial Behaviour of a Two-Zone The Strehl Ratio of a Two-Zone Element

  13. Conclusions - Two Zone Filter • Experiences a displaced focal spot from the focal plane • Large increase in sidelobes • Superresolution characteristics aren’t desirable • Semi agreement with Sales and Morris1 1. Sales., T.R.M., Morris.,G.M., Optics Comm. 156 (1998) 227

  14. Higher Dimensional Filters • If we increase N, the number of zones we find there are solutions for Superresolution • We examined a three-zone filter, and a five-zone filter. • We also generalised to a N-zone filter

  15. Binary N-Zone Filters • Consists of N concentric annuli called zones • We only consider equal area annuli, and zones of equal phase difference, normally Pi. • Indeed in the case of Pi, we get an expression for the axial point spread function

  16. Centered at Focal Spot Three-zone Filter PSF Centered at the Focal Plane Plots of the PSF at centered at different positions. The dashed line is the diffraction limit.

  17. Five-zone Filter Centered at Focal Spot Centered at the Focal Plane Plots of the PSF at centered at different positions. The dashed line is the diffraction limit.

  18. Conclusions • Three and Five zone filters exhibit similar behaviour: - Sidelobes displaced from the central spot - Focal Spot displacement increases • Spot size is about half the diffraction limited case – Amplitude filters S = 0

  19. Generalisation to N-Zone Filter • We showed following common properties are exhibited for N-Zone Filters when N is odd: - Sidelobes are increasingly displaced in proportion to 2N - Central Lobe displaced in proportion to N - No loss in Strehl Ratio - No increase in Spot Size

  20. Applications • Large scope for applications of filters - Confocal Microscopy - Scanning resolution and control depth of scanning - Optical Data Storage - Optical Lithography - Astronomy • Production is now much more possible than in the past 10 years

  21. Summary – The Future • Superresolution is the ability to resolve past the classical limit • Pupil plane filters provide a way to do this – in particular phase only filters • Superresolution appears to improve as the number of annuli is increased • Possible to control the position of the focal spot?

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