Sri Rama Prasanna Pavani, Ariel Libertun, Sharon King, and Carol Cogswell
Micro Optical – Imaging Systems Laboratory
University of Colorado at Boulder http://moisl.colorado.edu
Pavani et al - Univ. of Colorado, Boulder 1

 Transparent objects
(phase objects) modulate only the phase of light
 Square law detectors do not detect phase modulations
 Convert phase modulations into
“detectable” intensity modulations
Bright field
Pavani et al - Univ. of Colorado, Boulder 2

Phase contrast Diff. Interference Contrast
Convert phase modulations into “detectable” intensity modulations.
Digital Holography
 Quantitative phase for weak phase objects
 No phase wrapping
X Halo and shading-off
X Only for thin objects
 Quantitative phase after reconstruction
 No phase wrapping
X Polarization sensitive
X Only for thin objects
X Multiple images
Pavani et al - Univ. of Colorado, Boulder
 Quantitative phase after reconstruction
 Thick phase objects
 Single image
X Vibration sensitive
X Phase wrapping
3

 Quantitative phase imaging
Purpose:
Applicability:
 Thick, partially absorbing samples
 Polarization insensitive
Speed:
Miscellaneous:
 Single image
 Non-scanning (wide field)
 Non-Iterative
 Incoherent source
 Inexpensive
Pavani et al - Univ. of Colorado, Boulder 4

 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
Pavani et al - Univ. of Colorado, Boulder
0.2
(mm)
0.1
5

2D dot shift
1D dot shift
Pavani et al - Univ. of Colorado, Boulder 6

o Analytically relate deformation to the optical path length
( ( ) )

 ( ( ) )
  t t ( ( ) ) C


 r
 i o Consider a 1D phase object p(x) o Ray R from point A, after refraction, appears as if it originated from B n
1 o Deformation t(x) is the distance between A and B
A t(x)
Pavani et al, “Quantitative bright field phase microscopy”, to be sent to Applied Optics
Pavani et al - Univ. of Colorado, Boulder
B p(x) n
2
7

p ( x )



2
( n
1 n
1 n
2
 n
2
)
 t ( x ) dx

C


1
2
1D deformations After 1D integrations
Quantitative Phase
2D deformation
C m

1

C m


P x
2
( m

1 , d )

P x
2
( m , d ) P y
2
( m

1 , d )

P y
2
( m , d )

Pavani et al, “Quantitative bright field phase microscopy”, to be sent to Applied Optics
Pavani et al - Univ. of Colorado, Boulder 8

Quadratic phase
50
200
25
100
0 100 200
0
X 100
5
18
0 9 Calculated Phase
-5 0
1D deformations After 1D integrations
X 100
5
18
200
100
0 100 200
0
9
50
25
0
-5
Error
8
4
0
-4
-8
0 100 200
Pavani et al - Univ. of Colorado, Boulder
0
Peak error is 5 orders less than peak phase
9

Dot shift
Original pattern
Deformed pattern
16.54
Object:
Drop of optical cement
360
X,Y Deformations
3
0
180
Quantitative phase
Pavani et al - Univ. of Colorado, Boulder
40
30
20
10
0
360
0 240 480
-3
3
0
180
0 240 480
-4
10

Profilometer
Our method
Pavani et al - Univ. of Colorado, Boulder 11




Pavani et al - Univ. of Colorado, Boulder 12




Prof. Rafael Piestun
Prof. Gregory Beylkin
Vaibhav Khire
CDM Optics PhD Fellowship
National Science Foundation Grant No. 0455408
Pavani et al - Univ. of Colorado, Boulder 13

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
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
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J. W. Goodman, Introduction to Fourier Optics , (Roberts & Company, 2005)
M Pluta, Advanced Light Microscopy, vol 2: Specialised Methods , (Elsevier, 1989)
M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy”
Journal of Microscopy 214 (1), 7
–12 (2004)
C. Preza, "Rotational-diversity phase estimation from differential-interference-contrast microscopy images," J. Opt. Soc. Am. A 17 , 415-424 (2000)
Sharon V. King, Ariel R. Libertun, Chrysanthe Preza, and Carol J. Cogswell, “Calibration of a phase-shifting DIC microscope for quantitative phase imaging,”
Proc. SPIE 6443, 64430M (2007)
E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24 , 291-293 (1999)
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30 , 468-470 (2005)
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A. C. Sullivan, Department of Physics, University of Colorado, Campus Box 390, Boulder, CO 80309, USA and R. McLeod are preparing a manuscript to be called “Tomographic reconstruction of weak index structures in volume photopolymers.”
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“Optical coherence tomography,”
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BaroneNugent, E., Barty, A. & Nugent, K. “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc . 206 , 194 –203 (2002).
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Pavani et al - Univ. of Colorado, Boulder 14

 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
Pavani et al - Univ. of Colorado, Boulder 15

1 Dimensional analysis p ( x )
 tan n
1
(
 t r
( x

)
 i
) x

A
(from geometry) p ( x )
 tan sin

1


 n n
1
2 sin

 tan

1 n
1 t ( x ) dp ( x ) dx









 tan

1 p ( x )
 n
1 t ( x )







( n
1

1 ) dp ( x ) dx dp ( x ) dx








1

2 n
(Snell’s law, ) dx x

A

1
3

1
6
( n

1 )
3 
1
3





( n

1 )
2
3 n
2
 n
3
2










 dp ( x ) dx
 higher order terms






 p ( x ) dp ( x )

( n n
1
1
 n n
2
2
) t ( x ) dx p ( x )


2 I ( x )

C

2
1
(Taylor expansion)

( n n
1
1
 n n
2
2
) t ( x ) dx

I ( x )

C
2
C = 2 (C2 – C1) n
 n
1 n
2
Pavani et al - Univ. of Colorado, Boulder 16

M
2 Dimensional analysis
Apply 1D solution along x and y to obtain P x
2 and P y
2
P x
2
( m , 1 : N )

P
2
( m , 1 : N )

C m
P y
2
( 1 : M , n )

P ( 1 : M , n )

K n
C m

1

C m


P x
2
( m

1 , d )

P x
2
( m , d ) P
2
( m

1 , d )

P
2
( m , d ) ,

N
P y
2
( m

1 , d )

P y
2
( m , d )

P
2
( m

1 , d )

P
2
( m , d )
C m

1

C m


P x
2
( m

1 , d )

P x
2
( m , d )
P x
2
P 2
P y
2
( m

1 , d )

P y
2
( m , d ) .

P y
2
Pavani et al - Univ. of Colorado, Boulder 17