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Optical Designers meeting 22nd Sept 06a.r.harveyhw.ac.uk

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Optical Designers' meeting 22nd Sept '06 a.r.harvey_at_hw.ac.uk. 1. Wavefront coding: ... Optical Designers' meeting 22nd Sept '06 a.r.harvey_at_hw.ac.uk. 20. IR ... – PowerPoint PPT presentation

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Title: Optical Designers meeting 22nd Sept 06a.r.harveyhw.ac.uk


1
Wavefront coding a new dimension in optical
design
  • Andy R Harvey, Gonzalo Muyo, Bertrand Lucotte,
    Samir Mezouari
  • Engineering and Physical Sciences, Heriot Watt
    University, Edinburgh
  • Now with Visteon
  • Ewan Findlay
  • ST Microelectronics, Edinburgh
  • Dave Huckridge
  • QinetiQ, Malvern
  • Amritpal Singh
  • SAAB, Sweden
  • Andy Wood
  • Qioptiq, St Asaph

2
Summary
  • Wavefront coding
  • What is it?
  • Incorporation of WC into the optical design
    process
  • Applications
  • Increased depth of field
  • Mitigation of aberrations in low-cost lenses
  • The quid pro quo
  • The Physicists explanation of wavefront coding

3
Wavefront Coding what is it?
Integrated optical / digital system joint design
of optics and signal processing
  • Masks can be synthesised to alleviate sensitivity
    to optical aberrations
  • How?
  • What are the physical principles?
  • Is it useful?

4
Phase masks
  • Phase masks are synthesised by making a metric
  • MTF, PSF defined by an analytic expression
  • invariant with respect to defocus (or other
    aberration)
  • The most important masks are

Rectangular cubic
Generalised rectangular cubic petal
Radial quartic log
Optics Letters, 28, 10, pp 771-773, (2003)
5
Comparison between the PSF with and without CPM
6
Wavefront Coding MTF and PSF invariant to defocus
7
The additional parameter space of wavefront coding
Traditional Design
Fixed parameters Target metrics
Metrics
Lens Variables
WC Design
Fixed parameters Target metrics
Metrics
Lens Variables Mask variables
8
Example Applications
  • General imaging with increased depth of field
  • Low-cost lenses
  • Microscopy
  • Athermalisation of LWIR lens
  • Correction of astigmatism and field curvature in
    LWIR singlet

9
Experimental demonstrationwithout and with
wavefront coding
10
Athermalisation of LWIR imager
11
Defocus insensitive for thermal imaging
  • Thermal defocus is a severe problem for uncooled
    thermal imagers
  • Currently corrected with complex, high-cost lens
    systems

12
Traditional infrared lens system
  • MTFs contain zeros when ?T lt 7 ºC
  • Sensitive to temperature

13
Wavefront Coding in thermal imaging
  • No zeros in MTFs
  • Achieves complete athermalisation
  • MTF height reduced
  • No zeros in MTFs
  • Less sensitive to T
  • MTF height reduced

14
Simulated Image quality
Traditional IR 17 ºC
Traditional IR 60 ºC
Wavefront Coding 60 ºC
Diffraction limited
after Wiener filter
W20 5 l
15
Replace two-lens LWIR imaging lens with singlet
and wavefront coding
16
Simplification of LWIR F/1 f75mm Ge optical
system
  • From TWO ELEMENTS
  • Even asphere
  • Field flattener
  • Diffraction-limited
  • To SINGLET
  • Corrected for coma and spherical aberration
  • Off-axis performance limited by
  • Field curvature
  • Astigmatism

17
Correction of aberrations across FoV
  • 10 waves of aberrations
  • FoV of 9º
  • Presence of zeros in the MTFs
  • Large field curvature and astigmatism
  • Correction at the expense of bringing down MTF

18
Correction Petal phase mask (PPM)
  • After optimisation
  • Strength of mask a9.78mm and b-30.53mm
  • All MTFs practically identical

(0º, 0º)
(4.5º, 0º)
(3.2º, 3.2º)
19
PSFs across FoV
Variation of PSF in the image plane. Note This
image has a much greater resolution (1280 x 960)
than the detector (320 x 240)
20
IR singlet and phase mask
  • World first thermal imager with phase mask and
    singlet
  • Design and manufacture of Germanium phase mask
  • Uncooled detector
  • Reduced weight, size and cost
  • Partners SAAB, Qioptiq and QinetiQ

21
Implementation with a compound lens
  • In the ideal situation wavefront coding element
    is placed close to the exit pupil of a
    traditional lens design
  • This may not always be practical
  • Lens may need to be designed specifically for
    wavefront coding

22
Noise amplification
  • Antisymmetric phase mask ? Complex OTF
  • Noise gain not uniform, varies with
  • Direction
  • Defocus magnitude
  • Experimental realization with a cubic phase mask
    (height13mm)
  • Wiener filter restoration

23
Noise amplification
Noise gain Cubic phase mask
Noise gain Petal phase mask
24
Phase of the OTF
  • Antisymmetric phase masks introduce phase into
    OTF
  • OTF phase varies with defocus
  • Phase modulation of image components
  • Artefacts in the restored image
  • Shadows on edges

25
Rotationally symmetric phase mask
  • quartic and logarithmic phase masks
  • Inferior defocus tolerance symmetry means no
    phase effect
  • Advantages
  • Reduced artefacts
  • Easier to manufacture
  • Can be used without decoding

JOSA A, 23, pp1058-62 (2006)
26
Example quartic phase mask
Minor defocus
Extreme defocus
Moderate defocus
Without phase mask
With phase mask
27
Decomposition of OTF
  • OTF is integral of complex phasors
  • Defocus curls decomposed integral into circles in
    the complex plane
  • Explains nulls and phase reversals in OTF
  • Cubic Wavefront coding
  • For a given spatial frequency, OTF integral
    depicts a Cornu spiral
  • Defocus unwinds the spiral and produces no zeros
    in MTF

Optics Letters 30 (20) 2715-2717 Oct 15 (2005)
28
Decomposition of OTF
  • Radially Symmetric phase masks
  • For a given spatial frequency, OTF components
    depict a symmetric spiral
  • Small modulation of OTF with defocus
  • Phase of OTF always zero

29
Conclusions
  • For the ultimate performance do not use wavefront
    coding
  • Wavefront coding offers potential benefits where
    control of aberrations by traditional means is
    unattractive
  • Increased instantaneous depth-of-field
  • Focus-free
  • Focus-related aberrations
  • Relaxed lens tolerancing
  • Reduced lens count
  • Reduced light intensity at the detector (for a
    point source)
  • Wavefront coding is an additional variable in
    multi-parameter optimisation of imaging systems

30
Circular phase filters an example
  • Axial intensity in the presence of defocus w20
    and spherical aberration w40
  • Evaluate using the stationary phase approximation
    and
  • S. Mezouari and A. R. Harvey, Opt. Letters 28,
    pp771-773 (2003).
  • S. Mezouari, G. Muyo and A. R. Harvey, J. Opt.
    Soc. Am. A 23, 5 pp1-5 (2006).
  • SS Sherif, G Muyo, A R Harvey, Journal Of Modern
    Optics 52 (13) 1783-1788 Sep 10 (2005)

31
Defocused PSFs observed at different image planes
for various phase filters
32
PSF observed in optical system suffering from
coma aberration for various phase filters
33
Variation of PSFs With Aberrations
PSF remains practically unaffected
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