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

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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)
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Comparison between the PSF with and without CPM
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Wavefront Coding MTF and PSF invariant to defocus
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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
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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
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Athermalisation of LWIR imager
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Defocus insensitive for thermal imaging

• Thermal defocus is a severe problem for uncooled
  thermal imagers
• Currently corrected with complex, high-cost lens
  systems

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Traditional infrared lens system

• MTFs contain zeros when ?T lt 7 ºC
• Sensitive to temperature

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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

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Simulated Image quality
Traditional IR 17 ºC
Traditional IR 60 ºC
Wavefront Coding 60 ºC
Diffraction limited
after Wiener filter
W20 5 l
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Replace two-lens LWIR imaging lens with singlet
and wavefront coding
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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

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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

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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)
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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)
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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

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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

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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

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Noise amplification
Noise gain Cubic phase mask
Noise gain Petal phase mask
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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

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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)
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Example quartic phase mask
Minor defocus
Extreme defocus
Moderate defocus
Without phase mask
With phase mask
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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)
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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

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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

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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)

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