optical fourier techniques for medical image processing and phase

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Optics Communications 281 (2008) 1876–1888

Optical Fourier techniques for medical image processingand phase contrast imaging

Chandra S. Yelleswarapu, Sri-Rajasekhar Kothapalli, D.V.G.L.N. Rao *

Department of Physics, University of Massachusetts, Boston, MA 02125, USA

Received 6 March 2007; accepted 1 May 2007

Abstract

This paper briefly reviews the basics of optical Fourier techniques (OFT) and applications for medical image processing as well asphase contrast imaging of live biological specimens. Enhancement of microcalcifications in a mammogram for early diagnosis of breastcancer is the main focus. Various spatial filtering techniques such as conventional 4f filtering using a spatial mask, photoinduced polar-ization rotation in photosensitive materials, Fourier holography, and nonlinear transmission characteristics of optical materials are dis-cussed for processing mammograms. We also reviewed how the intensity dependent refractive index can be exploited as a phase filter forphase contrast imaging with a coherent source. This novel approach represents a significant advance in phase contrast microscopy.� 2007 Elsevier B.V. All rights reserved.

1. Introduction

Fourier theorem states that an arbitrary function withspatial period k can be decomposed into the sum of har-monic functions whose wavelengths are integral submul-tiples of k (i.e. k,k/2,k/3, . . .). Since k is considered as aspatial period, 1/k is called spatial frequency. It is knownthat far-field or Fraunhofer diffraction pattern of anaperture function is identical to its Fourier transform.The far-field distribution is nothing but the spatial fre-quency spectrum of the field distribution across the aper-ture [1–4]. If a lens is placed after the object, it willshorten the image plane distance and one will have theFourier spectrum at the back focal plane of the lens.Such an object lens is commonly referred as Fouriertransform lens and the process is called optical Fouriertransformation (OFT). OFT is a powerful tool widelyused for manipulation of optical data. With the availabil-ity of coherent sources, OFT is applied in a wide varietyof areas with unique features of parallel processing at thespeed of light. Applications of OFT in medicine and

0030-4018/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.optcom.2007.05.072

* Corresponding author.E-mail address: [email protected] (D.V.G.L.N. Rao).

biology are very broad and an extensive review ofOFT for medical imaging is therefore beyond the scopeof this paper. In this article we focus on applicationsof OFT to (1) medical image processing with particularreference to both analog and digital mammograms forearly detection of breast cancer, and (2) phase contrastmicroscopy to observe biological specimens.

The manipulation of spatial frequencies of two-dimen-sional images using OFT is well studied for applicationssuch as edge enhancement, character recognition, andimage correlation [5,6]. The basic concept of optical Fou-rier processing is shown in Fig. 1. A well collimated laserbeam is incident on the object (amplitude or phase) to beprocessed and the light bearing the object information isFourier transformed with a converging lens, mapping dif-ferent spatial frequencies to different regions in the backfocal plane. In the Fourier spectrum, low spatial frequen-cies occur at the center with high intensity and high spatialfrequencies at the edges with low intensity. Various imageprocessing techniques, such as low-pass, band-pass, high-pass, and phase-shift, are employed at the Fourier planeto process different spatial frequencies for various applica-tions. An inverse Fourier transform with another Fourierlens is used to image processed spatial frequencies on to

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532 nm laser

L2

Spatial Filter

NDF

CCDCamera

SLM or film mammogram

CL1

NDF1

L1

Fig. 2. Image processing with spatial filters. CL: collimating lens; L:Fourier lens; NDF: neutral density filter.

Original image Processed by filter 1

Processed by filter 2 Processed by filter 3

1

2

3

Fig. 3. (a) Spatial filters for image processing. 1 and 2 are high-pass filtersand 3 is low-pass filter. (b) Spatial filtering of binary image ‘‘E” using thesespatial filters.

CollimatedOpticalSource

Amplitudeor Phase Object

ProcessedImage

Filtered/modifiedSpectrum

SpatialFrequencySpectrum

OpticalFourierTransform

InverseFourierTransform

Fourier Plane: Spatial or Phase

Filter

Fig. 1. Optical Fourier processing scheme for amplitude as well as phaseobjects. Spatial filter for amplitude objects, whereas phase filter for phaseobjects.

C.S. Yelleswarapu et al. / Optics Communications 281 (2008) 1876–1888 1877

the CCD camera, so that the desired components of theimage are captured.

Optical Fourier processing is ideal to enhance the fea-tures of both amplitude and phase objects. For amplitudeobjects a spatial (amplitude) filter is employed at the Fou-rier plane while for phase objects a phase filter is used toalter the phase difference between high and low spatial fre-quencies. When it comes to application of OFT in medi-cine, the optical Fourier processing scheme suits well toprocess medical images like mammograms, hair-line frac-tures, etc. Similarly optical Fourier processing is widelyused in biology – as phase contrast imaging to observephase objects.

2. Spatial filtering for medical image processing

Processing of mammograms by enhancing the desiredfeatures of interest to the radiologist will effectively helpin early detection of breast cancer [7–9]. Mammography,the current ‘gold standard’ for breast cancer screening,has been shown to be effective in screening breast cancer[10–12]. Abnormalities detected in mammography can beclassified as masses, lesions, and microcalcifications. Fea-tures such as microcalcifications are often buried in thebackground of soft dense breast tissue in a mammogramresulting in low contrast between these essential featuresand the background. More over, breast density can makeit even more difficult to detect these microcalcifications inthe mammogram. Therefore, mammogram image analysisis a challenging task both for radiologists and researchersinvolved in the image processing field [11]. Application ofappropriate image processing techniques is required inreading mammograms for better sensitivity and specificityof clinical cancer diagnosis [12–15]. Microcalcifications inthe mammogram correspond to high spatial frequenciesin the Fourier spectrum, due to their small in size and dif-fuse in nature, and occur at the edges with low intensity.Thus, they can be conveniently separated at the Fourierplane from low spatial frequencies which are due to thedense soft tissue. When the undesired low spatial frequen-cies are filtered out, the processed image displays only highspatial frequency components, thus making microcalcifica-tions visible to the naked eye.

Fig. 2 shows a schematic of the conventional 4f config-uration for the image processing with various spatial filters.A diode pumped solid state Nd:YAG laser with 532 nm

and output power 10 mW is expanded to a spatially uni-form beam. Light transmitted through the object is focusedby the Fourier lens. At the Fourier plane, various spatialfilters are used for blocking undesirable components.Through an inverse Fourier transformation, the filteredfrequency components in the Fourier plane are imagedon to a CCD camera.

For demonstration, we fabricated several spatial filters toselectively display various spatial frequency bands of the bin-ary test object ‘‘E”. Fig. 3a shows the spatial filters used in theexperiment while Fig. 3b shows the processed images. Usingthe filters 1 and 2, edge enhancement is obtained by blockinglow spatial frequency components. Two very thin filamentsare purposely placed in the top left corner of the originalimage and are indicated by arrows in the Fig. 3b. They arebarely visible in the original image, but can be clearly seenin the processed images with filters 1 and 2. On the otherhand, filter 3 blocks the high frequency components. Thus,the processed image becomes soft (no sharp edges). In thiscase, the filaments become more blurry as they correspondto the high spatial frequencies.

The procedure is applied for systematic investigation ofmammogram images. Fig. 4 shows the results of a mammo-gram processed with filter 1 shown in Fig. 3a. The region ofabnormal pathological changes is buried in the dense breasttissue background as shown in Fig. 4a. Fig. 4b is the pro-cessed image captured by the CCD camera displaying micro-calcifications corresponding to the high spatial frequency

Fig. 4. Processing of mammogram using a spatial filter. (a) Original mammogram where the desired features of interest are buried in the background ofsoft breast tissue. (b) Filtered image displaying only the features of interest.

B - State

M - State

~ 570 nm

ThermalDecay, ms - sec

~ 412 nm, ns

Fig. 5. (a) Photocycle of bacteriorhodopsin molecule. (b) Equivalent twolevel model.

1878 C.S. Yelleswarapu et al. / Optics Communications 281 (2008) 1876–1888

band after eliminating the surrounding dense breast tissuewhich corresponds to the low spatial frequencies.

However, there are some disadvantages with the simplespatial filtering technique. When the object mammogram ischanged the spatial frequency spectrum at the Fourier planewill be different due to the changes in the density and regionof interest in the mammogram. So each time the size of thespatial filter has to be modified accordingly and has to be pre-cisely placed at the Fourier plane. Thus, it is a not a real-timeprocessing as the filter is not all-optically and continuallycontrollable. To overcome these difficulties, researchers havedeveloped several nonlinear filtering techniques for self-adaptive and real-time computing. Organic and biologicalmolecules, photorefractive polymers, and liquid crystalsare used as the nonlinear medium.

Kato and Goodman demonstrated logarithmic filteringby placing a halftone contact screen (periodic array of vig-netted dots on a flexible support) in the input plane of acoherent optical system [16]. The Fourier spectrum is pro-cessed with an appropriate spatial filter and is inverse Fou-rier transformed. The processed image displays the desirednonlinear function of the original intensity. More recently,Babkina et al. used an acousto-optic modulator at the Fou-rier plane to perform spatial frequency filtering where theacoustic wave in the paratellurite crystal forms a gratingpattern [17]. When the incident optical beam interacts withthe grating, the light is diffracted into zero order and firstorder. By varying the modulator driving frequency, edgeenhancement effect is observed in the diffracted beam inreal-time. On the other hand hybrid processing techniquesare also proposed and demonstrated in the literature wherethe object information is Fourier transformed with a lasersource and spatial filters (generated digitally in the com-puter) are displayed on the spatial light modulated(SLM) placed at the focal plane for real-time processing.The SLM can be electrically addressed SLM [18], opticallyaddressed SLM [19] or bR film [20]. Such a hybrid process-ing technique is also used for phase contrast imaging of livebiological specimens more recently [21].

3. Photoinduced anisotropy for medical image processing

Photoinduced anisotropy properties of various materialshave been used for spatial filtering. Two groups indepen-dently exploited photoinduced anisotropy and photoin-duced dichroism properties of bacteriorhodopsin (bR)films for real-time image processing. While our group dem-onstrated a self-adaptive all-optical Fourier image process-ing system using photoinduced dichroic characteristics [22],Korchemskaya’s group exploited photoinduced anisotropyfor real-time selective image processing [23]. On the otherhand, several other groups exploited similar photoinducedpolarization rotation properties of azobenzene dye dopedliquid crystal and polymer films for spatial filtering [24–26]. Simply by placing a polarizer sheet at the Fourierplane, Ferrari et al. demonstrated phase visualization andedge enhancement [27]. Most recently, Menke et al. demon-strated optical image processing using photoinducedanisotropy property of pyrrylfulgide [28].

The basic principle of spatial filtering is same in all theseprocessing schemes – intensity dependent polarization rota-tion in combination with an analyzer will selectively transmitthe desired spatial frequency band. Here we will briefly dis-cuss about such basic filtering operation using bR and itsapplication to processing clinical mammograms and Papsmears [29]. The photocycle of biological photomembrane

Actinic beam intensity, W/cm2

10-8 10-7 10-6 10-5 10-4 10-3 10-20

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1.0

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2.5

3.0

Pola

riza

tion

rota

tion,

ang

le in

deg

rees

10-1

Fig. 7. Dependence of photoinduced polarization rotation on actinicbeam intensity with constant probe beam intensity [29].

Probe beam intensity, W/cm2

10-6 10-510-4 10-3 10-2 10-1 100 101

Pola

riza

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rota

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ang

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deg

rees

0

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Fig. 8. Polarization rotation induced in the probe beam as its intensity isincreased under constant actinic beam [29].


bR is shown in Fig. 5a. In its stable B state, upon the absorp-tion of a photon within the broad absorption with a maxi-mum at 570 nm, the bR molecule goes through aphotochemical cycle of several short lived intermediatestates J, K, L and then to the long-lived M state with anabsorption peak at 412 nm within 50 ls. The lifetime of theM state can be altered by several orders of magnitude byaltering the reprotonation process. The M state moleculesare thermally transformed into the initial B state in millisec-onds or they can go back directly to the initial B state within200 ns by absorption of a blue photon. The most relevantstates in the bR photocycle for our experiments are the Band M states and can be viewed as a two level system asshown in Fig. 5b. The bR can be switched between B ¡ Mstates at relatively low powers of milliwatts.

The bR film is initially isotropic as the molecules arerandomly oriented. As it is placed between a crossed pola-rizer (V) and analyzer (H) arrangement, as shown in Fig. 6,no probe beam light gets through. When a linearly polar-ized light (actinic beam) with polarization at 45� to the ver-tical is incident on the film, due to the photoinduceddichroism, some light transmits through as a result of acti-nic induced polarization rotation of the probe beam. Theamount of polarization rotation is a function of the actinicbeam intensity and is given in Fig. 7.

Fig. 8 shows the experimental data on the degree ofrotation of probe beam polarization as a function of probebeam intensity under constant actinic beam intensity of10 mW/cm2. For low probe beam intensities, the degreeof rotation is large and it gradually goes to zero as theintensity is increased. This aspect is used for spatial filter-ing. In the Fourier spectrum low spatial frequencies occurat the center with high intensity and high spatial frequen-cies occur at the edge of the spectrum with low intensity.Therefore, from Fig. 7, we can say that low spatial frequen-cies acquire no polarization rotation as they are at highintensity, whereas high spatial frequencies will have largepolarization rotation due to their low intensity. Thus, byselectively rotating analyzer, we can image desired featuresof interest of an image. In bR, switching between B and Mstates are used to create the photoinduced anisotropy. Sim-ilarly in azobenzene molecules, trans–cis isomerizationstates are exploited, whereas pyrrylfulgide operatesbetween its two states – bleached state (E-form) and col-ored state (C-form) [28].

PolarizerAnalyzer

Polarization rotator

VH

Actinic beam

Probe beam

Fig. 6. Schematic of the experimental setup for the measurement ofphotoinduced polarization rotation.

The concept of spatial filtering using photoinducedanisotropy in bR films is applied for medical image pro-cessing. A schematic of the experimental setup for medicalimage processing is shown in Fig. 9. A linearly polarized(vertical) probe beam carrying the medical image informa-tion is Fourier transformed on to the bR film with a lens.As this information passes through the bR film in the pres-ence of actinic illumination, it acquires a range of polariza-tions of different orientations depending on the intensitiesin the Fourier spectrum. Thus, there is a correspondencebetween spatial frequency–intensity–polarization and eachspatial frequency band is encoded with a unique polariza-tion. The spatial filtering is accomplished by selectivelyrotating the analyzer such that undesired spatial frequen-cies are blocked. When the analyzer is at right angles tothe input beam polarization, the low frequency compo-nents that experience no polarization rotation are blockedby the analyzer. On the other hand high spatial frequencycomponents corresponding to edges of the object experi-ence polarization rotation due to their low intensity. Thus,the unblocked spatial frequencies are transmitted through

12

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1 0

4

9

3

11

1

2

Fig. 9. Medical image processing with bR films. 1: Beam from 532 nmdiode pump laser; 2: microlens and pin hole filter; 3: collimating lens; 4:vertical polarizer; 5: input image; 6: Fourier lens; 7: nonlinear optical bRfilm; 8: inverse Fourier lens; 9: analyzer with horizontal axis; 10: processedimage; 11: actinic 532 nm beam; 12: 45� polarizer.


the analyzer and imaged on to the CCD camera to yieldedge enhancement. By rotating the axis of the analyzer,one can filter out undesirable components enhancing thefeatures of interest.

Fig. 10. The experimental results of medical image proces

Clinical mammograms and Pap smears are processedwith this experimental system and the results are shownin Fig. 10. Fig. 10a shows the original mammogram.Fig. 10b is the processed image clearly displaying themicrocalcification clusters which are not visible in the ori-ginal mammogram. Low spatial frequencies correspondingto the dense soft breast tissue are filtered out. Fig. 10cshows the original Pap smear where the bright spots repre-sent the cells. Both normal (small spots) and abnormal cells(large cluster) are visible in the original picture. In the pro-cessed image, Fig. 10d, the normal cells are filtered outretaining only the abnormal cells. This is achieved by selec-tively filtering out high spatial frequency components(rotation of the analyzer from the crossed position) in theFourier spectrum.

4. Fourier holography for medical image processing

In holography, the object and reference plane wavesare interfered in the medium to record the hologram.When the recorded hologram is illuminated by the refer-ence wave or another plane wave preserving the angleof incidence, the entire information of the object (bothamplitude and phase) is reconstructed. If the recording

sing: mammogram (top) and Pap smear (bottom) [29].


is done between the Fourier spectrum of an object and asimple plane wave, then the recorded hologram is referredas Fourier hologram. By recording and reconstructing theFourier hologram one can retrieve both amplitude andphase information of the object. This technique isexploited for spatial filtering and image processing. Fein-berg used barium titanate photorefractive material todemonstrate edge enhancement in real-time by recodingand reading gratings of object information [30]. This prin-ciple is used by Ochoa et al. to identify defects in a peri-odic mask using barium silicon oxide as photorefractivecrystal [31]. Okamoto et al. presented a real-time opticalsystem to enhance nonlinear diffraction efficiency of holo-graphic gratings written in a bR film [32]. The gratingpattern is read using Fourier transform of a periodic pat-tern to be inspected. In the readout process the diffractionefficiency of the grating depends on the intensity of thereading beam. Therefore, using suitable reading beamintensity, only the defect component is displayed. Simi-larly, two-beam coupling in photorefractive materials areexploited to spatially amplify the desired frequency bandof the Fourier spectrum [33]. Unlike in the conventional4f spatial filtering system where the undesired spatial fre-quency components are selectively blocked at the Fourierplane, this technique does not discard any of the incidentimage information. By selectively overlapping the desiredspatial frequency band with the pump beam, only the

L2L1

Ar-Kr laser 568 nm

E BS2

E

M2

Object

NDF BE

CCD M1

BS1

Fig. 11. Experimental arrangement for study of edge enhancement usingtransient Fourier hologram recorded in the bR film. M: Mirrors; BS: beamsplitters; L: lenses.

Fig. 12. Image processing of clinical mammogram using Fourier holography. (the clusters of microcalcifications are clearly identified [34].

desired features of the image are amplified in intensityby a factor of 1000 thereby increasing the contrastbetween the desired and undesired information.

Fourier holography in bacteriorhodopsin (bR) films isapplied for processing medical images. Transient Fourierholographic gratings based on photoinduced isomerizationproperties of bR films are used to perform spatial filteringfor detection of microcalcifications in real-time [34]. Fig. 11shows the experimental arrangement of Fourier hologra-phy where the Ar–Kr ion laser beam is expanded and splitinto two beams. The object beam (mammogram or binaryobject E), is Fourier transformed by the lens L1 of 20 cmfocal length. At the Fourier plane the bR film is placedfor real-time processing of spatial frequency information.The reference beam obtained with the beam splitter BS1overlaps the Fourier transform of the object beam on thebR film thereby recording a Fourier hologram. When theobject beam is blocked, the reference beam performs thereconstruction of the recorded Fourier hologram. The dif-fraction efficiency is maximum when the object beam inten-sity matches that of the reference beam intensity. At eitherlow or high intensity region of the object beam, the diffrac-tion efficiency decreases. Thus, the desired spatial fre-quency components can be selected by matching theirintensity to that of the reference beam.

The processing results of clinical screen-film mammo-gram are shown in Fig. 12. High spatial frequency compo-nents of the object are recorded by matching the intensityof reference beam to the intensity of high spatial frequencyband. The recording process takes about 5 s. When theobject beam is blocked, the reference beam performsthe reconstruction of the recorded hologram displayingthe spatial frequencies whose intensity in the Fourier spec-trum is matched to the reference beam intensity. Thus, theradiologist can easily scan for desired microcalcificationclusters by rotating the variable attenuator that controlsthe reference beam intensity.

A significant feature of this technique is that theenhanced components in the processed image can be

a) Mammogram with region of interest marked. (b) Processed image where

Fig. 13. Transient display of spatial frequency information of grating resolution chart captured at times: (a) t = 0 s and (b) t = 5 s [34].

1E-6 1E-5 1E-4 1E-3

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Input Intensity (Joules)

a

b

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de

Fig. 14. Power limiting characteristic display of sample [35].


separated in time scale, which enables the radiologist tomonitor different pathological features in the mammogramat a different time scale. Since different spatial frequencybands correspond to different intensities, all the bands existsimultaneously with different diffraction efficiencies. How-ever, the optimum diffraction efficiency occurs only for aselected band of frequencies which match with the refer-ence beam intensity. Thus, one can distinguish between dif-ferent spatial frequencies as they reveal at different times;the band of frequencies with optimum efficiencies lastlonger. We used a resolution chart (USAF negative target,Edmund Optics) to observe this phenomenon. As shown inFig. 13 at time t = 0 we can observe all the frequencygroups (A – low frequency group, B – middle frequencygroup and C – high frequency group) but at time att = 5 s only the frequency group B which matches the ref-erence beam intensity appears clear while other frequencygroups vanish. This could be a potential advantage to theradiologist to view various features in the mammogramat different time scales.

5. Nonlinear transmission for medical image processing

Transmission of nonlinear optical materials is yetanother phenomenon which ideally suits for spatial filter-ing and medical image processing. Recently it is demon-strated that any nonlinear transmission (power limiting)mechanism can potentially be used for image processing[35]. Nonlinear optical principles such as two photonabsorption, excited state absorption, nonlinear scattering,self-focusing, etc. exhibit reduced transmittance for highinput intensities while offering linear transmittance at lowintensities, as shown in Fig. 14 for phthalocyanine sample.Therefore, intensity dependent nonlinear transmission canbe used to filter out undesired spatial frequency bands inthe Fourier spectrum of the image. The spatial frequency

distribution at the Fourier plane can be categorized intodifferent intensity bands and low spatial frequencies atthe center with high intensities and high spatial frequencieson the edges with low intensities. At low incident beamintensity all the spatial frequencies are transmitted throughthe phthalocyanine sample without any filtering. As theincident intensity is increased above the threshold valuefor power limiting, the low spatial frequencies begin todiminish as they occur at high intensities. Thus, the powerlimiting curve for a given phthalocyanine sample facilitatesthe calculation of required input intensities to obtain thedesired band of spatial frequencies.

Spatial filtering with nonlinear optical material is illus-trated in Fig. 15 using a binary test object ‘‘E”. The powermeasurements recorded by the power meter reveal the opti-cal limiting characteristics as shown in Fig. 14 while the

Fig. 15. Processed images showing the edge enhancement of the object E. (i)–(iv) The points where the processed images are captured using the CCDcamera [35].


CCD captured the edge enhancement effects of the objectat the corresponding incident beam energies. When theintensities are below the limiting threshold, the absorptionis in the linear regime and the entire information of theobject is transmitted through the sample without any pro-cessing as shown in Fig. 15a. The corresponding positionon the power limiting curve is marked as (a) in Fig. 14.As the input intensity is increased to the power limitingthreshold, the intensity in the low spatial frequency bandis sufficient enough to trigger excited state absorption inthe sample and begin to diminish as shown in Fig. 15b.When input intensity is increased further, the intensity oflow spatial frequency band is beyond the power limitingthreshold. So in this region phthalocyanine moleculesundergo excited state absorption and thus low spatial fre-quency band is completely attenuated. But at the same timethe intensity of high spatial frequencies striking the sampleare well below the power limiting threshold and thus trans-mitted without being absorbed as shown in Fig. 15c. Anear perfect edge enhancement of the object is observedwhen the input intensities are well above the limitingthreshold as depicted in Fig. 15d and e.

This type of spatial filtering technique is relatively userfriendly compared to the other image processing techniquesthat are discussed above – a spatial mask is used at theFourier plane as in the case of conventional image process-ing or a reference beam (actinic beam) is needed to performthe image processing or requires cross polarization. Whilespatial mask is cumbersome and requires precise align-ment, the Fourier holography technique that employs ref-erence beam need to be performed on a vibrationisolation table as interference is involved. In contrast spa-

tial filtering using nonlinear optical transmission can beperformed using two lenses and a neutral density filter.Apart from its simplicity the technique is self-adaptive tothe background intensity (amount of dc) of image. As afringe benefit, when the same experimental setup is usedfor both power limiting experiment and optical image pro-cessing, as in the case of image bearing intense laser beam,the sensitive detectors are potentially protected by blockingthe intense low spatial frequencies, while detecting theessential features of the image by detecting the weak highspatial frequencies.

Depending on the nonlinear material either one or twobeams needs to be employed. Xuan et al. exploited twophoton absorption and stimulated Raman scattering innonlinear material like acetone and CS2 for contrastimprovement and contrast reversal [36]. Thoma et al. usedphotocontrolled transmission properties of bR films foredge enhancement of images [37]. Theoretical simulationsshow that the transmittance of bR films at 568 nm can becontrolled by 413 nm pump beam. Similar results areobtained experimentally and the scheme is applied for med-ical images [38]. For the case of bR, the transmission of ablue probe beam (442 nm) in a bR film can be controlledwith a yellow actinic beam (568 nm). Fig. 16 illustratesthe experimental setup and the corresponding results.Intensity dependent transmission characteristics are stud-ied using the experimental setup shown in Fig. 16a. Trans-mittance of the blue beam through the bR film is measuredas a function of the intensity of the control yellow beam.The results displayed in Fig. 16b shows that the local trans-mittance of the film for blue beam decreases significantlywhen the intensity of the control yellow beam is increased.

bRfilm

He-CdLaser442 nm

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Fig. 16. Experimental setup of nonlinear transmission through bR film with control of actinic beam. The results are displayed in the plot.

NDF2

L1L2

bR film

L3

NBF

CCDCamera

442 nm laser

Inlet

568 nm Laser

SLM or Film mammogram

CL2

CL1

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Fig. 17. Schematic of image processing using nonlinear absorption in bRfilms. L: converging lens; NBF: a narrow band filter to block 568 nm atCCD plane; CL: collimation lenses; NDF: neutral density filters. Inset:Fourier spectrum and the spatial overlap of two beams at the bR film plan[38].


Fig. 17 shows the experimental setup for medical imageprocessing based on this mechanism. The informationbearing blue beam (442 nm) is Fourier-transformed to the

Fig. 18. (a) Film mammogram with magnified R

bR at the focal plane and the desired spatial frequenciesare selectively blocked by illuminating the film with a568 nm control beam. Since different spatial frequencycomponents are spatially separated in the Fourier plane,the physical location of the yellow control beam on thebR film determines the components blocked. If high spatialfrequency information is desired, then the low frequencycomponents are blocked by focusing the control beam atthe center of the Fourier spectrum.

Fig. 18 shows the image processing of clinical screen-film mammogram and the corresponding processed imagewhich display only microcalcifications, not visible to thenaked eye in the original mammogram.

As digital mammography is becoming popular, we alsoperformed image processing of digital mammograms. Anelectrically addressed spatial light modulator (SLM) is usedto facilitate the interface between digitally stored mammo-gram in the computer and the optics used in the experi-ment. The collimated He–Cd 442 nm laser beamilluminates the SLM and the output of the SLM is a coher-ent optical signal bearing the image being displayed on theSLM. Fig. 19 shows the original and the corresponding

OI and (b) its processed image of ROI [38].

Fig. 19. Region of interest of a digital mammogram and its processed image showing only microcalcifications [38].


processed images of a digital phantom containing simu-lated microcalcifications buried in the gray backgroundand a clinical digital mammogram. In presence of yellowcontrol light beam, low spatial frequencies (gray back-ground) are blocked and the reconstructed image showsonly high spatial frequencies.

6. Phase contrast imaging of biological specimens

Spatial filtering techniques are used for enhancing thefeatures of amplitude objects where part of the Fourierspectrum is either blocked or transmitted depending onthe filtering scheme. Mostly these filters can be describedas amplitude or binary filters. In the conventional 4f spatialfiltering scheme, however, if the amplitude object isreplaced with a phase object and the spatial filter with aphase filter, the phase filter only alters the phase of partof the Fourier spectrum. Such a processing scheme is noth-ing but phase contrast imaging which is widely used toobserve phase objects.

Phase objects are transparent – they provide no contrastwith their environment and alter only the phase of thewave. The optical thickness of such objects generally variesfrom point to point due to changes in either the refractiveindex or physical thickness or both. Since eye cannot detectthe changes in phase variations, phase objects are invisibleto the naked eye. However, if an additional phase differ-ence is created between the undeviated (low spatial fre-quencies) and deviated (high spatial frequencies) light,then they interfere either constructively or destructively(depending on the amount of phase added) thereby con-verting the phase variation into amplitude contrast. Phasecontrast imaging was developed in 1933 by Zernike [39] toobserve phase objects. He used a phase plate to create a p/2phase difference between the undeviated light and the lightdiffracted by the object thereby transforming minute varia-tions in phase of the object into corresponding changes inthe image contrast. This principle is exploited in the phase

contrast microscope which is widely used in teaching andresearch labs to view high-contrast images of transparentspecimens, such as living cells (usually in culture), microor-ganisms, thin tissue slices, lithographic patterns, fibers,latex dispersions, glass fragments, and subcellular particles(including nuclei and other organelles).

Several alternative concepts for phase contrast imagingare demonstrated to avoid the complications with the usageof phase plate as a phase filter. It is difficult to place thephase plate at the exact location so that the required phaseshift is induced between low and high spatial frequencies,and manufacturing the phase plate is also not trivial. Liuet al. used photorefractive crystals at the Fourier plane tointroduce uniform phase shift to low spatial frequencycomponents [40]. A C-cut LiNbO3:Fe crystal sheet servedas the phase filter and good phase contrast images areobtained. Gluckstad worked out both theoretical andexperimental ways to improve imaging of phase objects[41,42]. As an extension to Zernike phase contrast configu-ration, they showed that phase-only encoding utilizing full-range (0–2p) yields phase-only imaging with high energyefficiency.

The optically addressed spatial light modulator(OASLM) also serves as a nonlinear filter when placed atthe Fourier plane and edge enhancement and phase con-trast imaging are demonstrated [43]. The required phasechange is obtained through the dependence of the extraor-dinary index of refraction of OASLM on voltage. Simi-larly, Komorowska et al. used an OASLM made of aplanar nematic liquid crystal layer sandwiched between aphotoconducting polymer and a polyimide orienting layerand performed phase contrast imaging [44]. The inducedphase modulation is proportional to the intensity of theincident light on the OASLM.

Popescu et al. developed Fourier phase microscopy bycombining phase contrast microscopy and phase shiftinginterferometry (PSI) to quantify the phase shifts inducedby the phase objects [21]. Fourier transform of the object

Fig. 20. Fourier phase contrast imaging of Paramecium. (a) Bright fieldimage of live Paramecium. (b) Corresponding Fourier phase contrastimage.


is projected onto the surface of a reflective programmablephase modulator (PPM) and the phase of diffracted lightis shifted into four increments of p/2 with respect to theaverage field (undeviated or dc), as in typical PSI measure-ments. After recording four interferograms, the phase shiftassociated with the object is evaluated qualitatively at eachand every point of the field of view.

Nonlinear optical materials are also used as phase filters.Castillo et al. utilized the Kerr-type nonlinear property ofbacteriorhodopsin film for self-induced Zernike-type filterand obtained phase contrast images [45]. Sendhil et al.exploited the intensity dependent refractive index of zinctetraphenyl porphyrin for phase contrast imaging [46]. Inthese methods, the zero order of the Fourier spectruminduces intensity dependent refractive index changesthereby modifying its phase. Since only the zero orderinduces a phase shift and not the higher orders, a phase fil-ter is created and phase contrast imaging is performed.

Photothermal induced birefringence property of dyedoped twisted nematic liquid crystals are exploited forself-adaptive all-optical Fourier phase contrast imagingof biological species [47]. When the dye doped twistednematic liquid crystal cell is placed at the back focal planeof a converging lens, high intensity low spatial frequenciesinduce local liquid crystal molecules into isotropic phase,whereas low intensity high spatial frequencies are notintense enough and molecules in this region remain in ananisotropic phase. Liquid crystal molecules in the aniso-tropic phase add certain amount of phase to the incidentpolarized light, whereas the molecules in the isotropicphase do not add any additional phase. Therefore, the highspatial frequencies acquire an additional p/2 phase as theytransmit through the self-induced anisotropic phase oflocal liquid crystal molecules. The low spatial frequencies,however, transmit through the self-induced isotropic phaseof liquid crystal molecules without acquiring any phase dif-ference. This leads to a relative phase difference of p/2between high and low spatial frequencies, primary criteriafor phase contrast imaging, at the exit plane of liquid crys-tal cell.

Fig. 21. (a) Bright field image and (b) Four

Fig. 20 illustrates images of paramecium. Paramecia areunicellular microorganisms belonging to the protoctistphylum Ciliophora. Members of this phylum (ciliates) arecharacterized by their cigar or slipper shape and externalcovering of continuously beating, hair-like cilia, and thesefine structures in particular are not always easy to visualizewith bright field microscopy unless the rest of the specimenis out of focus. The bright field image obtained with oursystem (Fig. 20a) shows the distinguishing specimen outlineand oral groove of the paramecium but not much more.Fig. 20b displays the Fourier phase contrast image wherethe outline of the Paramecium is identifiable, and the exter-nal fine hair-like structures called cilia can be seen at theposterior end (top of the image). The feeding structure,the oral groove and other internal structures are clearlyvisible.

We also applied the Fourier phase contrast technique toview onion peel. Onion cells from the skin of an onion bulb

ier phase contrast image of onion cells.


are commonly used for early training comparisons betweenplants and animals. The thin layer of cells is so translucentthat phase contrast or staining is needed for viewing.Fig. 21a shows a bright field image of such a preparationof onion cells, the walls and nuclei are visible but that isgreatly enhanced with the phase contrast image seen inFig. 21b.

7. Conclusion

We reviewed the applications of various optical spatialfiltering techniques with specific applications for processingof mammograms and phase contrast imaging of biologicalspecimens. For medical image processing each filteringtechnique has its own merits and demerits. Employing aspatial mask at the Fourier plane is the simplest of all,but the same filter size may not work for all mammograms.However, if a spatial light modulator is used at the Fourierplane, then the filtering using a digital spatial mask is moreconvenient. Therefore, all-optical self-adaptive spatial fil-tering is an ideal choice for real-time image processing.One disadvantage with most of these filtering techniquesis the need for a second beam: (1) Photoinduced anisotropy– the amount of polarization rotation that can be inducedis very small (�5� in bR) and hence the rotation of analyzeris very critical. Therefore, this technique can be of practicalimportance only for materials with large polarization rota-tion. (2) Fourier holography – the major drawback is therequirement of vibration isolation as it involves interfer-ence. However, this type of image processing scheme hasthe additional ability of displaying different pathologicalfeatures of interest in time scale. During the readout pro-cess, when the spatial frequency information is unfolding,a movie can be recorded using a fast CCD camera. Theradiologist can view the movie at his leisure – look at thefeatures corresponding to different spatial frequencies oneby one in sequence or freeze the frame to concentrate ona particular feature. (3) Nonlinear transmission – the focalspot size of the control beam on the bR film has to beadjusted for different mammograms. However, such adrawback can be avoided when a single beam induced non-linear transmission is exploited in commercially availablereverse saturable absorption materials. As digital mam-mography is becoming more prominent, any of these opti-cal processing techniques can be used for digitalmammograms by employing spatial light modulator atthe object plane.

Finally, optical Fourier processing techniques usingcoherent source offer several distinct advantages over con-ventional screening of mammograms using white light; thesame facts also hold for phase contrast microscopy. Asthe deviation angle depends on the wavelength, the mono-chromaticity in the Fourier techniques facilitates clear andwell resolved spatial frequency bands for the Fourier pro-cessing. Intensity of the laser source makes object featuresbright and clearly visible. As such high spatial frequenciesare enhanced and can be observed with good contrast.

Further in the case of phase contrast imaging, the highdegree of phase coherence preserves phase retardationintroduced by the phase filter. Thus, the phase informationcan be converted to amplitude with good contrast. Phasequantization studies using Fourier phase microscopyalready demonstrated potential applications for basicresearch. Thus, optical Fourier transform in medicine andbiology is a promising area of research leading to significantadvances in both basic science as well as technology.

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optical fourier techniques for medical image processing and phase

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