Deconvolu)on	  Spa)al	  Light	  Interference	  Microscopy	  	  for	  Subdiﬀrac)on	  Imaging	  of	  Live	  Cells	  S.	  Derin	  Babacan	  	  	  	  Zhuo	  Wang	  	  	  	  	  Minh	  Do	  	  	  	  	  Gabriel	  Popescu	  Outline	  • Overview	  of	  SLIM	  • Proposed	  complex	  ﬁeld	  deconvoluDon	  (dSLIM)	  – Complex	  ﬁeld	  degradaDon	  – “Sparse”	  imaging	  model	  – Algorithm	  • Experimental	  results	  – ResoluDon	  increase	  – Live	  cell	  imaging	  S.	  Derin	  Babacan	  2	  SpaDal	  Light	  Interference	  Microscopy	  • Combines	  phase	  contrast	  microscopy	  	  	  	  	  	  	  with	  holography	  • Record	  4	  intensity	  maps	  with	  	  	  	  	  	  	  addiDonal	  spaDal	  modulaDons	  	  • Uniquely	  determines	  the	  phase	  •	  No	  staining	  or	  tagging	  •	  Speckle-­‐free	  •	  Very	  fast	  acquisiDon	  •	  Very	  high	  signal-­‐to-­‐noise	  raDo	  (0.3	  nm	  spaDally	  and	  0.03	  nm	  temporally)	  •	  QuanDtaDve	  imaging	  of	  transparent	  objects	  S.	  Derin	  Babacan	  3	  

SpaDal	  Light	  Interference	  Microscopy	  SpaDally	  coherent	  light	  source	  U (x, y) = |U (x, y)| exp [iΦ(x, y)]UnscaZered	   U0ScaZered	  = |U0 | exp [−iφ0 ]U1 (x, y) = |U1 (x, y)| exp [iφ1 (x, y)]Recorded	  Intensity	  I(x, y, φ0 ) = |U0 |2 + |U1 (x, y)|2 + 2|U0 ||U1 (x, y)| cos (φ1 (x, y) + φ0 )Magnitude	   m(x, y) =Extracted	  Phase	  �|U1 (x, y)||U0 |m(x, y) sin(φ1 (x, y))Φ(x, y) = arg
1 + m(x, y) sin(φ1 (x, y))S.	  Derin	  Babacan	  �4	  Complex	  Field	  DegradaDon	  • Both	  phase	  and	  magnitude	  can	  be	  uniquely	  determined	  (complex	  image	  ﬁeld)	  U (x, y) = |U (x, y)| exp [iΦ(x, y)]• However,	  observaDons	  are	  degraded	  Ũ (x, y) = U (x, y) ∗ h(x, y) + n(x, y)
Observed	  Field	  S.	  Derin	  Babacan	  Original	  Field	  Imager	  	  Point	  Spread	  FuncDon	  	  (PSF)	  Noise	  5	  Complex	  Field	  DeconvoluDon	  • QuanDty	  of	  interest	  is	  the	  phase	  	  – Assume	  constant	  magnitudes	  Complex	  Deconvolu)on:	  Data	  ﬁdelity	  	  	  (reconstruc)on	  constraints)	  Sharp	  image	  *	  PSF	  ≈	  observed	  image	  Ψ̂(x, y) = argmin
Ψ(x,y)
Phase	  EsDmate	  Regulariza)on	  (image	  model)	  12�Ψ̃(x,y)−h(x,y)∗Ψ(x,y)
�+βR(Ψ(x, y))22σ

Noise	  level	  Observed	  	  Phase	  Image	  Target	  Phase	  Image	  Ψ(x, y) = exp [iΦ(x, y)]S.	  Derin	  Babacan	  6	  Phase	  Imaging	  of	  Biological	  Specimen	  • Phase	  imaging	  – relaDve	  insensiDve	  to	  the	  uniform	  background	  – highly	  sensiDve	  to	  object	  boundaries	  (High	  contrast	  around	  edges)	  • Biological	  specimen	  (e.g.,	  cells)	  – The	  specimen	  contains	  very	  ﬁne,	  small-­‐scale	  structures	  and	  dynamics	  • Construct	  the	  image	  model	  to	  represent	  this	  ﬁne	  structure	  with	  sharp	  boundaries	  S.	  Derin	  Babacan	  7	  Image	  Model	  • Sparsity	  principle:	  The	  image	  can	  be	  transformed	  to	  a	  domain	  where	  it	  is	  sparse	  	  Filtering	  Histogram	  65432
10−4S.	  Derin	  Babacan	  −202
Phase values

464x 10

7
Number of pixels (log10)

Histogram	  Number of pixels (log10)

76

Most	  elements	  near	  zero	  54Only	  a	  few	  are	  large	  3210−4−202Phase values

464x 108	  Image	  Model	  Diﬀerent	  transforms	  capture	  diﬀerent	  image	  characterisDcs	  4x 10
2.6
2.4
2.2
2
1.8
1.6
1.4
1.210.8

Very	  small	  features	  	  S.	  Derin	  Babacan	  Filtering	  Filtering	  Filtering	  3000

3000

3000

2500

2500

2500

2000

2000

2000

1500

1500

1500

1000

1000

1000

500

500

500

000

−500

−500

−500

−1000

−1000

−1000

Medium-­‐size	  features	  	  Lines,	  curves,	  …	  9	  Algorithm	  Ψ̂(x, y) =�

HT H + σ 2

DTk Ak D k

k=1• EsDmate	  the	  image	  Current!
image!
estimate!

L��−1HT Ψ̃(x, y)

Regulariza)on	  using	  	  Transform	  Sparsity	  Apply!
filter!
D1!

Compute!
A1!

Apply!
filter!
D2!

Compute!
A2!

!"
!
!

!"!
!

Apply!
filter!
DL!

Compute!
AL!

Conjugate !
Gradient!
Iterations!

Noise! PSF!
variance! h!
"2!

New!
image!
estimate!

SLIM!
Image!

• EsDmate	  the	  “sparsity”	  coeﬃcients	  (locaDons	  and	  strength	  of	  local	  spaDal	  acDvity)	  Babacan,	  et	  al.	  Biomed.	  Op+cs	  Express	  	  (2011)	  S.	  Derin	  Babacan	  10	  Experiments	  –	  ResoluDon	  SLIM	  PSF	  FWHM	  ≈	  540	  nm	  	  dSLIM	  PSF	  FWHM	  ≈	  238	  nm	  	  10.9Original

0.8

dSLIM≈	  2.3x	  resolu)on	  increase	  	  0.7
0.6
0.5
0.4
0.3
0.2
0.1
0−0.8S.	  Derin	  Babacan	  Babacan,	  et	  al.	  Biomed.	  Op+cs	  Express	  	  (2011)	  −0.6

−0.4

−0.2

00.2

Distance (μm)

0.4

0.6

0.811	  Experiments	  –	  ResoluDon	  200nm	  Microbeads	  ≈	  550nm	  apart	  	  SLIM	  SLIM
dSLIM

1

Barely	  resolved	  dSLIM	  0.8
0.6Resolved	  0.4
0.2−1S.	  Derin	  Babacan	  −0.5
00.5Distance (µm)

1Babacan,	  et	  al.	  Biomed.	  Op+cs	  Express	  	  (2011)	  12	  Live	  cell	  imaging	  Hippocampal	  neuron	  SLIM	  S.	  Derin	  Babacan	  dSLIM	  13	  Live	  cell	  imaging	  SLIM	  S.	  Derin	  Babacan	  dSLIM	  14	  Dynamic	  live	  cell	  imaging	  SLIM	  S.	  Derin	  Babacan	  dSLIM	  15	  Dynamic	  live	  cell	  imaging	  dSLIM	  SLIM	  Time	  	  SLIM	  dSLIM	  SLIM
dSLIM

10.8
0.6
0.4
0.20ï1

ï0.5

00.5
Distance (µm)

11Barely	  resolved	  0.8Resolved	  0.60.40.20ï1

ï0.5

00.5
Distance (µm)

1ï0.5

00.5
Distance (µm)

11
0.8
0.6
0.4
0.2
0
ï1

S.	  Derin	  Babacan	  16	  Conclusions	  • dSLIM	  is	  a	  novel	  deconvoluDon	  method	  for	  complex	  image	  ﬁelds	  acquired	  by	  interference	  microscopy	  – Linear	  process	  in	  complex	  image	  ﬁelds	  – High	  SNR	  by	  SLIM	  -­‐>	  accurate	  PSF	  esDmates	  – Phase	  images	  of	  biological	  specimen	  can	  be	  accurately	  modeled	  using	  sparsity	  principles	  • High	  spaDal	  resoluDon	  quanDtaDve	  imaging	  below	  diﬀracDon	  	  S.	  Derin	  Babacan	  17