dighologr&imgproc.pdf

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DIGITAL HOLOGRAPHY

AND

IMAGE PROCESSING


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L. Yaroslavsky,Ph.D., Dr. Sc. Phys&Math,

Professor

Dept. of Interdisciplinary Studies,

Faculty of Engineering, Tel Aviv

University, Tel Aviv, Israel

www.eng.tau.ac.il/~yaro


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Digital holography and image processing: twins

born by the computer era

Digital holography:

- computer synthesis, analysis and simulation ofwave fields

Digital image processing:

- digital image formation;

- image perfection;

- image enhancement for visual analysis;

- image measurements and parameter estimation;

- image storage; image visualization


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New qualities that are brought to optical information

systems by digital computers and processors:

Flexibility and adaptability.The most substantial advantage of digital computers as compared with analog electronic and optical

information processing devices is that no hardware modifications are necessary to reprogram digital

computers to solving different tasks. With the same hardware, one can build an arbitrary problem

solver by simply selecting or designing an appropriate code for the computer. This feature makes

digital computers also an ideal vehicle for processing optical signals adaptively since, with the help of

computers, they can adapt rapidly and easily to varying signals, tasks and end user requirements.

Digital computers integrated into optical information processing

systems enable them to perform arbitrary signal transformations

Acquiring and processing quantitative data contained in optical

signals, and integrating optical systems into other informational

systems and networks is most natural when data are handled in

digital form.In the same way as in economics currencies are general equivalent, digital signals are general

equivalent in information handling. A digital signal within the computer that represents an optical one

is, so to say, purified information carried by the optical signal and deprived of its physical

integument. Thanks to its universal nature, the digital signal is an ideal means for integrating

different informational systems.


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Laser

Collimator

Beam spatial

filter

Lens

Microscope

Object table

Digital

Photo-

graphic

camera

Computer

One of the main drawbacks of

microscopy: the higher is the spatial

resolution, the lower is depth of focus.

This problem can be resolved by

holography.

Holography is capable of recording 3-D

information. Optical reconstruction is

then possible with visual 3-D observation.

Drawbacks of optical holography:

-Intermediate step

(photographic development

of holograms) is needed.

-Quantitative 3-D analysis

requires bringing in

additional facilities

Radical solution: optical holography withhologram recording by electron means

(digital photographic cameras) and digital

reconstruction of holograms. This is the

principle of digital holographic

microscopy.

Digital Holographic/Interferometric Microscopy


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Hologram

Fourier PlaneFirst focal plane Second focal plane

Digital Reconstruction of Holograms (Equivalent optical setup)


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Hologram

sensor

Preprocessing

of digitized

hologram

Image

reconstruction

(DFT/DFrT)

Image

processing

Hologram

Analog-to-

digital

conversion

Output

image

Computer

Digital Holography: Digital Reconstruction of Holograms

M.A. Kronrod, N.S. Merzlyakov, L.P. Yaroslavsky, Reconstruction of a Hologram with a Computer,

Soviet Physics-Technical Physics, v. 17, no. 2, 1972, p. 419 - 420


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Computer simulation of coherent imagingCase study: Speckle noise in coherent imaging systems

Hologram

Hologram sensor

Measuring hologram

orthogonal/

amplitude-phase

components:

- Limitation of the

hologram size

- Limitation of the

hologram component

dynamic range

- Hologram signal

quantization

Reconstruction of

the hologram

Reconstructed image

Diffusely

reflecting

object

Reflected

wave front


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Statistical characterization of speckle noise in

coherent imagingL. Yaroslavs ky, A. Shefler, Statistical characterization of speckle noise in coherent imaging systems, in: OpticalMeasurement Systems for Industrial Inspection III, SPIEs Int. Symposium on Optical Metrology, 23-25 June 2003,

Munich, Germany, W. Osten, K. Creath, M. Kujawinska, Eds., SPIE v. 5144, pp. 175-182

2-D array that specifies

amplitude component of

the object wave front

Generating 2-D array of

pseudo-random numbers

that specify the phase

component of the object

wave front

Computing

objects wave

front

Simulating wave

front propagation

(DFT, DFrT)

Introducing signal

distortions:

-Array size

limitation-Dynamic range

limitation

-Quantization

Simulating wave

front

reconstruction

(IDFT, IDFrT)

Comparing

reconstructed and initial

wave fronts; computing

and accumulation of

noise statistical

parameters

Continue

iterations

?

Yes

NoOutput data

Illustrative examples of simulated images: a) - original

image; b) - image reconstructed in far diffraction zone from

0.9 of area of the wave front; c) - image reconstructed in far

diffraction zone from 0.5 of area of the wave front; d) -

image reconstructed in far diffraction zone after limitation of

the wave front orthogonal components in the range.

Computer model


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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.2

0.4

0.6

0.8

1

GrLv 1/8

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Reconstructed images for different

limitations of the wave front measured area

Speckle contrast as a function limitations of the

wave front measured area

Speckle noise and sensors size in hologram reconstruction


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Mathematical

model of the

object

Complex

amplitude of

object

wave field

Computation of

mathematical

hologram:

-Fourier Transform

-Fresnel Transform

-Composition of

spherical waves

Coding

computer

generated

hologram

for recording

Recording

computer

generated

hologram

Digital-to-analog

conversion

Hologram

usage model

Computer

Digital Holography:

Synthesis of Holograms and Diffractive Optical elements


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Computer generated holograms

Binary CGH

Gray scale CGH

Reconstructed image

M.A. Kronrod, N.S. Merzlyakov, L.P. Yaroslavsky, Computer Synthesis of Transparency Holograms, Soviet Physics-

Technical Physics, v. 13, 1972, p. 414 - 418.


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Computer generated holograms for 3-D holographic

display in 70-th:

L.P. Jaroslavski, N.S. Merzlyakov,

Stereoscopic Approach to 3-D Display Using

Computer-Generated Holograms, Applied

Optics, v.16, No. 8, 1977, p. 2034.

Reconstructed

images

Programmed

diffuser hologram

method.

L. Yaroslavskii,

N. Merzlyakov,

Methods of

Digital

Holography,

Cons. Bureau,

1980

Hologram

Object


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Opto-electronic correlators with Computer Generated

Holograms

F F

1-st

Fourier

lens

Parallel

laser

light

beam

Input

image

Template

TV

camera

Correlati

on plane

F F

2-nd

Fourier

lens

Spatial

Light modulator

Computer

Joint

spectrum

plane

Input image

Computer controlled nonlinear

media and reflective matched

filter

Correlation

output

Parabolic

mirror

Nonlinear computer controlled optical

correlator with a parabolic mirror

Joint transform correlator


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Target localization in clutter in multi-component

imagesL. Yaroslavsky, Optimal target location in color and multi component images, Asian Journal of Physics, Vol. 8, No 3

(1999) 355-369


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Optimal adaptive correlators: detection of

microcalcifications in mammograms

Detection and enhancement of microcalcifications in a mammogram

Input mammogram


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Object tracking in video sequencies: examples

Tracking

fetus

movements

in

Ultrasound

movie

For details see http://www.eng.tau.ac.il/~yaro

Leonid P. Yaroslavsky, Ben-Zion Shaick Transform Oriented Image Processing Technology for Quantitative Analysis of Fetal Movements in Ultrasound

Image Sequences. In: Signal Processing IX. Theories and Applications, Proceedings of Eusipco-98, Rhodes, Greece, 8-11 Sept., 1998, ed. By S.

Theodorisdis, I. Pitas, A. Stouraitis, N. Kalouptsidis, Typorama Editions, 1998, p. 1745-1748


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Face detection in complex imagesBen-Zion Shaick, L. Yaroslavsky, Object Localization Using Linear Adaptive Filters, 6th Fall Workshop,

Vision, Modeling And Visualization 2001 (Vmv01), November 21-23, 2001, Stuttgart, GermanyStuttgart,

Germany, November 21-23, 2001, pp. 11-17


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Digital image processing in 70-th:

Mars-4 and Mars-5 (1973), Venera-9, Venera-10 (1975)T.P. Belikova, M.A. Kronrod, P.A. Chochia, L.P. Yaroslavsky, Digital Processing of

Martian Surface Photographs from " Mars-4" and " Mars-5", Kosmicheskiye Issledovaniya, v. 13, iss. 6, 1975, p. 898-906

First panoramic images from Venus surface: Venera-9, Venera-10

Images from Mars orbiter Mars-4/5: before and after rectification


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First color image of Martian surface synthesized

by computer processing (Mars-4, Mars-5, 1973)D.S. Lebedev, M.K. Naraeva, A.S. Selivanov, I.S. Fainberg, L.P. Yaroslavsky, Synthesis of Color Images of the Surfaceof Mars from Photos, obtained from the Space Station "Mars-5", Doklady of the USSR Academy of Sciences, ser.

Mathematics and Physics,v. 225, No. 6, 1975, p. 1288-1292.


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Multi component image restoration:

adaptive linear filters


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Restoration of high resolution satellite imagesL. Yaroslavsky, High Resolution Satellite Image Restoration with the Use of Local Adaptive Linear Filters, Report on

Keshet Program, July, University Dauphine, Ceremade, Paris,1997

Spot-image: before Spot-image: after


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Image resampling and geometrical transformations:

efficient discrete sinc-interpolation algorithmsL. Yaroslavsky, Boundary effect free and adaptive discrete sinc-interpolatioon, Applied Optics, 10 July 2003, v. 42, No. 20,p.1- 10


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Direct Fourier method for inverse Radon transform:

polar-to- Cartesian coordinate spectrum conversion with

discrete sinc-interpolation(L. P. Yaroslavsky, Y. Chernobrodov, Sinc-interpolation methods for Direct Fourier Tomographic Reconstruction, 3-d Int. Symposium,

Image and Signal Processing and Analysis, Sept. 18-20, 2003, Rome, Italy)

Object

Projections

Projection spectra

Interpolated 2-D

object spectrum

Reconstructed

image


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Spectrum/correlation analysis with sub-pixel

resolution


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Image geometrical transformations with discrete

sinc-interpolation

Radius

Angle

Cartesian

to polar

Polar to

Cartesian


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Noisy image (a) and a result of the rotation and denoising withsliding window DCT sinc-interpolation and denoising (b).

a)

b)

Adaptive image resampling and denoising


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Image restoration and enhancement: nonlinear

filtersL. Yaroslavsky, Nonlinear Filters for Image Processing in Neuromorphic Parallel Networks, Optical Memory andNeural Networks, v. 12, No. 1, 2003

Noisy image, stdev = 20, Pn=0.15

Iterative SCSigma-filter . Wind.

5x5, Evpl=Evmn=15; 5 iterations


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Initial image SIZE(Evnbh(Wnbh5x5,2,2))-filter HIST(W-nbh)-filter

Nonlinear filters: Image enhancement


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Initial image

RANK(KNV

(Wnbh15x15;113))

RANK(Wnbh15x15)

RANK(EV

(Wnbh15x15;10,10))

Nonlinear Filters: Image Enhancement

Local histogram equalization: Wnbh, EV-nbh and KNV-nbh


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Local P-histogram equalization: color images

(blind calibration of CCD-camera images)


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Computer synthesis and display of stereoscopic images


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Computer generated stereo from video

Endoscopy Entertainment

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