DIGITAL HOLOGRAPHY

AND

IMAGE PROCESSING

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

ProfessorDept. of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv

University, Tel Aviv, Israelwww.eng.tau.ac.il/~yaro

Digital holography and image processing: twins born by the computer era

Digital holography:- computer synthesis, analysis and simulation of wave fieldsDigital image processing:- digital image formation;

- image perfection;

- image enhancement for visual analysis;

- image measurements and parameter estimation;

- image storage; image visualization

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 processingsystems 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.

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 with hologram recording by electron means (digital photographic cameras) and digital reconstruction of holograms. This is the principle of digital holographic microscopy.

Digital Holographic/Interferometric Microscopy

HologramFourier PlaneFirst focal plane Second focal plane

Digital Reconstruction of Holograms (Equivalent optical setup)

Hologram sensor

Preprocessing of digitized hologram

Image reconstruction(DFT/DFrT)

Image processing

Hologram

Analog-to-digital

conversion

Outputimage

Computer

Digital Holography: Digital Reconstruction of HologramsM.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

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

Hologram

Hologram sensorMeasuring 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

Statistical characterization of speckle noise in coherent imagingL. Yaroslavs ky, A. Shefler, Statistical characterization of speckle noise in coherent imaging systems, in: Optical Measurement Systems for Industrial Inspection III, SPIE’s 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 object’s 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

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

GrLv 1/82/83/84/85/86/87/88/8

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 sensor’s size in hologram reconstruction

Mathematicalmodel 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

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.

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

Opto-electronic correlators with Computer Generated Holograms

F F

1-stFourier

lens

Parallel laser light beam

Input image

Template

TV camera

Correlation plane

F F

2-ndFourier

lens

SpatialLight 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

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

Optimal adaptive correlators: detection of microcalcifications in mammograms

Detection and enhancement of microcalcifications in a mammogram

Input mammogram

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

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

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 ofMartian 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

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 Surface of 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.

Multi component image restoration: adaptive linear filters

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

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

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

Spectrum/correlation analysis with sub-pixel resolution

Image geometrical transformations with discrete sinc-interpolation

Radius

Angle

Cartesian to polar

Polar to Cartesian

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

Image restoration and enhancement: nonlinear filtersL. Yaroslavsky, Nonlinear Filters for Image Processing in Neuromorphic Parallel Networks, Optical Memory and Neural Networks, v. 12, No. 1, 2003

Noisy image, stdev = 20, Pn=0.15

Iterative SCSigma-filter . Wind. 5x5, Evpl=Evmn=15; 5 iterations

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

Nonlinear filters: Image enhancement

Initial image

RANK(KNV(Wnbh15x15;113))

RANK(Wnbh15x15)

RANK(EV(Wnbh15x15;10,10))

Nonlinear Filters: Image EnhancementLocal histogram equalization: Wnbh, EV-nbh and KNV-nbh

Local P-histogram equalization: color images(blind calibration of CCD-camera images)

Computer synthesis and display of stereoscopic images

Computer generated stereo from video

Endoscopy Entertainment