Quantitative phase estimation with a bright field microscope

1
Quantitative phase estimation with a bright field
microscope
Sri Rama Prasanna Pavani, Ariel Libertun, Sharon
King, and Carol Cogswell Micro Optical Imaging
Systems Laboratory, ECE, University of Colorado
at Boulder http//moisl.colorado.edu
Frontiers in Optics 9/18/2007
2
Phase imaging What? How?

• Transparent (phase) objects modulate only the
  phase of light
• Convert phase modulations into detectable
  intensity modulations

• Quantitative phase for weak phase objects
• No phase wrapping
• Halo and shading-off
• Only for thin objects

• Quantitative phase after reconstruction
• No phase wrapping
• Polarization sensitive
• Only for thin objects
• Multiple images

• Quantitative phase after reconstruction
• Thick phase objects
• Single image
• Vibration sensitive
• Phase wrapping

• No quantitative phase

3
Our method

• Amplitude mask in the field diaphragm
• Pattern is imaged on the sample
• Phase object distorts the pattern
• Record the distorted pattern
• Analytical formula calculates phase

Vs
0.2 0.1
(mm)
0.4 0.2
0 0.2 0.4
(mm)
(mm)
4
Our method 1D

• Analytically relate deformation to the optical
  path length
• Consider a 1D phase object p(x)
• Ray R from point A, after refraction, appears as
  if it originated from B
• Deformation t(x) is the distance between A and B

Normal
Tangent
n2
p(x)
n1
A
B
t(x)
Pavani et al, Quantitative structured-illuminatio
n phase microscopy, submitted to Applied Optics,
June 07 Pavani et al, Structured-illumination
quantitative phase microscopy, CMB4, COSI 2007
5
Our method 2D
1D deformations
After 1D integrations
C1 C2 . . CN
Quantitative Phase
2D deformation
K1 K2 KN
Pavani et al, Quantitative structured-illuminatio
n phase microscopy, submitted to Applied Optics,
June 07
6
Simulation
X 100
18 9 0
5 0 -5
Calculated Phase
Quadratic phase
50 25 0
50 25 0
200 100
200 100
After 1D integrations
1D deformations
X 100
18 9 0
5 0 -5
0 100 200
0 100 200
Error
8 4 0 -4 -8
(nm)
Peak error is 5 orders less than peak phase
Error
0 100 200
7
Experimental Results
X,Y Deformations
Dot shift
Original pattern
3 0 -3
360 180
0 240 480
Deformed pattern
3 0 -4
360 180
16.54
0 240 480
Quantitative phase
40 30 20 10 0
Profilometer Our method
Object Drop of optical cement
360 180
480 240 0
8
Spatial Resolution

• Size and the spacing between dots
• Dots sampling the object must obey Nyquist
• Resolution enhancement by shifting

d
s
M
M
shift right
shift down
shift diagonally




N
N

• If dot size diffraction limited spot size,
  quantitative phase imaging with the same
  resolution as a bright field image is possible

9
Spatial Resolution

• Size and the spacing between dots
• Dots sampling the object must obey Nyquist
• Resolution enhancement by shifting

d
s
M
M
shift right
shift down
shift diagonally




N
N

• If dot size diffraction limited spot size,
  quantitative phase imaging with the same
  resolution as a bright field image is possible

• Full resolution single image phase imaging with
  multi-colored dots

10
Phase resolution
Dot shift

• Smallest detectable change in path length
• Minimum deformation

w detector pixel width M magnification

• Trapezoidal numerical integration

s
x
x
Example
lt
w 7µm s 1µm
n1 1.5 n2 1
M 100x NA 0.9
Depth of field 753nm
11
Conclusion

• Described wide field, full resolution
  quantitative phase imaging in a bright field
  microscope
• Phase is calculated from deformation using an
  analytical formula
• Conservative calculations with a 100x objective
  predict a phase resolution of 155nm

12
Acknowledgements

• Prof. Rafael Piestun
• Prof. Gregory Beylkin
• Vaibhav Khire

CDMOptics PhD Fellowship
National Science Foundation Grant No. 0455408
13
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14
Applications and Future work

• Industrial inspection, biological imaging
• Extracting information from axial deformation
• Extending the depth of field of the system
• Fabrication of an amplitude mask with higher
  spatial resolution

15
Our method How?
1 Dimensional analysis
(from geometry)
(Snells law,
)
(Taylor expansion)
C 2 (C2 C1)
16
Our method How?
M
2 Dimensional analysis
N
Apply 1D solution along x and y to obtain
and
P2
17
Metrology - Cubic phase mask
120 80 40 0
360 180
480 240 0
Deformation
Quantitative OPL profile
140 70 0
Cubic phase mask
360 180
480 240 0
Deformation
Quantitative OPL profile