High-resolution full-field optical coherencemicroscopyusing a Mirau interferometer for the quantitative
imaging of biological cells
Tulsi Anna, Vishal Srivastava, Dalip Singh Mehta,* and Chandra ShakherLaser Applications and Holography Laboratory, Instrument Design Development Centre,
Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India
Optical coherence tomography (OCT) is a powerfultool for high-resolution cross-sectional tomographicimaging for internal microstructures of biologicaltissues and materials [1–3]. It is realized in time-domain OCT (TD-OCT) and frequency-domainOCT (FD-OCT), but in comparison to TD-OCT, theFD-OCT provides high-speed and high-resolutionimaging [1–5]. FD-OCT is further carried out in twoways: first using a broadband light source and spec-trometer [spectral domain-OCT (SD-OCT)] and sec-ond using a narrowband swept source and a singlepoint detector [swept-source OCT (SS-OCT)] [1–6].The detection system for SS-OCT is simpler and anarrowband light source facilitates the longer depthscans in comparison to SD-OCT [5,6]. Various SS-OCT systems have been reported, but most of themrequire the lateral mechanical scanning for full-fielddetection [6–9]. Recently, full-field SS-OCT and het-
erodyne low coherence interferometric systems usingan acousto-optic tunable filter (AOTF) and modula-tors with completely nonmechanical scanning havebeen investigated [10,11].
The depth (axial) and lateral (transverse) resolu-tions along with dynamic range, measurementspeed, and the center wavelength of the light sourceare important parameters which govern the perfor-mance of the OCT systems [2,3]. The axial resolution,governed by the coherence length, is inversely pro-portional to the optical bandwidth of the light source,whereas the transverse resolution depends on theNA of the objective lens and focusing a beam to asmall spot size. The conventional OCT primarily wasusing low NA objective lenses to generate cross-sectional images resulting in sufficient axial resolu-tion and low transverse resolution for the cellularimaging. To improve the transverse resolution, highNA objectives were used in OCT which was namedoptical coherence microscopy (OCM) [2,3,12,13]. Theuse of high NA objectives in OCM leads to bettertransverse resolution, and in this case enface imag-
ing is more effective than cross-sectional imaging. InOCM, the unwanted scattered light coming from thesample is rejected by coherence gating. Because ofthe high contrast and improved imaging depth,OCM becomes more useful in comparison to OCT.OCM uses both the time-domain and frequency-domain techniques, but it has a major disadvantageas the light beam is scanned point by point mechani-cally over the sample (i.e., X–Y–Z scanning) [2,3].
Recently, various full-field optical coherence micro-scopy (FF-OCM) systems has been developed inwhich the sample is entirely illuminated, and inthe image field, two-dimensional (2D) interferencefringes were recorded using a CCD camera/detector,which makes the lateral scan redundant [14–23]. Ingeneral, FF-OCM is carried out with the Michelsoninterferometer with low coherence source. However,later on in various FF-OCM systems, different con-figuration such as Linnik and Mirau interferometers[14–23] have been used. Most of these systems use aLinnik interferometer, of course these can provide ul-trahigh resolution such as transverse resolution ofabout 0:7 μm, but one has to adjust the two micro-scopic objectives independently. Some of the above-mentioned microscopes use the achromatic phaseshifter and piezoelectric translators in one of thearms of the interferometer and hence requires me-chanical scanning. Further, in these systems white-light sources are used leading to high axial andtransverse resolution, but these systems suffer froma dispersion effect, therefore, they require dispersioncompensating plates in both the arms and make thesystem complicated. Along with the above mentionedOCM systems, the holographic systems for the quan-titative phase measurements of biological cells havebeen suggested [24–27]. Further, the various othertechniques have also been reported for the quantita-tive phase imaging of a live cell, such as Fourierphase microscopy [28], a tomographic phase micro-scopy [29], optical diffraction tomography [30] of mi-crostructures, and live cells [31]. These quantitativephase measurement methods are very encouraging,but most of the methods use lasers as a light source,which leads to noise due to speckles and the highpower of the lasers may damage the cells. Some ofthese are based on a Mach–Zehnder interferometerand again uses a mechanical scanning device forphase shifting.
A coaxialMirau interferometer for the OCT systemwas originally reported by Dobroiu et al. [32] thatmakes the highly miniaturized device possible andhas been applied for the profilometry of rough sur-faces. For the OCM systems, as discussed earlier, ahigh axial and transverse resolution is required forthe cellular level imaging. In this paper we have de-monstrated a FF-OCM system based on aMirau-typeinterferometric objective lens (with high magnifica-tion) using a swept-source system for the quantitativeimaging of biological cells. The swept-source systemwas realized in the wavelength range from 815 to870 nm using a combination of a superluminescent
diode (SLD) as a broadband light source and anAOTFas a frequency-scanning device, hence no mechanicalscanning isneeded.Thedetailed characteristics of theswept-source system are available in the paper byDubey et al. [10]. The Mirau objective lens is usedin the interferometric arm to produce the interferencesignal which is detected by the CCD camera. Interfer-ence between the backscattered signals from the dif-ferent layers of the object and reference beam wasrecorded by tuning the wavelength in a regular inter-val, and the interferograms were stacked in longitu-dinal direction. The Fourier-transform technique hasbeen used formeasurement of amplitude andphase ofthe object. The present system uses a highmagnifica-tion Mirau-interferometric objective lens and a rela-tively larger bandwidth light source to achieve a highresolution in cellular level imaging. The use of a Mir-au interferometer is advantageous over conventionalinterferometric systems because of its common pathgeometry. It is a compact interferometric unit whichleads to high phase stability and insensitive to exter-nal vibration. The present systemuses parallel detec-tion and can measure enface images without X‒Yscanning with high axial and transverse resolutionand is easy to align.
2. Theoretical Background of the High-ResolutionFF-OCM
The FF-OCM system was constructed by using aswept source, a Mirau interferometer, and a CCD de-tector as shown in Fig. 1. The working principle isbased on a low coherence interferometry, the sameas in conventional OCT, and a detailed theoreticalbackground of the FF-OCM system is given in [3].The interference pattern is observed only if the opti-cal path difference (OPD) between the reflected sig-nal from the sample and reference arm is within thecoherence length of the source. The recorded inten-sity Iðx; y; kmÞ can be expressed as [3,33]
Iðx; y; kmÞ ¼ Sðx; y; kmÞfðRR þ RSÞþ 2
ffiffiffiffiffiffiffiffiffiffiffiffiffiRRRS
pcosð2kmΔzðx; y; kmÞ
þΔΦðx; y; kmÞÞg; ð1Þ
Fig. 1. (Color online) Schematic of a high-resolution FF-OCMsystem based on the Mirau-interferometric objective lens.
where km is the optical wavenumber, the detector ele-ments are indexed by m ∈ f1;Mg, (where M is thenumber of spectral samples), Sðx; y; kmÞ is the sourcespectral density, and RR and RS represent thereflected light from the reference and sample arms,respectively. Δz is the OPD between the sample andreference arm andΔΦðx; y; kmÞ is the interferometricphase difference associated with the detector signal.Further, the OPD is related to the ΔΦðx; y; kmÞ andrefractive index of the sample as [34]
ΔΦðx; y; kmÞ ¼2πλ0
Δzðx; y; kmÞ
¼ 4πλ0
tðx; yÞfnðx; y; kmÞ − 1g; ð2Þ
where λ0 is the source center wavelength, i.e.,842:5nm of the broad band light source. nðx; y; kmÞis the refractive index of the object, which is a func-tion of the position and wavelength of light, andtðx; yÞ is the corresponding physical thickness of theobject under test at a particular position. From theknowledge of the phase map, the OPD (height map)and 2D refractive index profile of the biological objectcan be obtained. Depth information of the sample canbe obtained by discrete Fourier transform of thedetector signals [33]
I½zn� ¼XMm¼1
I½x; y; km�e−ðj2πð2kmznÞÞ; n ∈ f1;Mg: ð3Þ
The factor of 2 in the kernel exponent ensures therecovery of single-sided distances, andM is the num-ber of spectral samples. With a single reflector in thesample arm, Eq. (3) gives three peaks and the originof the three peaks can be obtained by computing theFourier transform of Eq. (1):
IðznÞ ¼ Γ2ðznÞ ⊗ fRRδðznÞ þ RSδðznÞþ 2
ffiffiffiffiffiffiffiffiffiffiffiffiffiRRRS
pðδðzn þΔzÞ þ δðzn −ΔzÞÞg; ð4Þ
where Γ2ðznÞ is the envelope of the coherence func-tion which is the Fourier transform of the sourcespectral density. The first and second term in the par-entheses on the right-hand side describes the auto-correlation noise from the reference and samplearm, respectively, also called DC artifacts. The finalterm is due to interference between light returningfrom the reference mirror and the sample and pro-vides the coherence signal of the sample’s depth in-formation. The image depth with a 6dB roll-off point
can be calculated by lnð2Þπ
λ20δλnavg
(where λ0 is the centerwavelength, navg is the average refractive index ofthe sample [assuming that navg ¼ 1:35] and δλ ¼1:5nm is the instantaneous line width of the filteredlight), which comes out to be ∼80 μm [3].
An important particularity of FF-OCM systemsproducing enface images is that the axial resolution
may not exclusively depend on the coherence lengthof light but it also depends on the NA of the objectivelens which is formally identical to conventional mi-croscopy. Hence the axial resolution of the presentsystem is determined by both the coherence lengthof the illumination source and the objective NA andcan be expressed as [3]
δz ≈�NA2
navgλ0þ navgπ2 ln 2
�Δλλ20
��−1; ð5Þ
where Δλ is the FWHM of the source spectrum andfrom Eq. (5) the δz is calculated as 2:5 μm for Δλ ¼48:38nm and NA ¼ 0:55 (50×).
The high transverse resolution of the systemcan be obtained by using a large NA and focusinga beam to a small spot size, and for OCM it can beexpressed as [3] ΔX ≈ 0:46λ0=NA:The FF-OCMsystem works on reflection mode and hence theMirau-interferometric objective lenses are used forilluminating the sample as well as for collecting thebackscattered light from the sample. The focal lengthof different Mirau objective lenses used in thepresent study, i.e., 10× (NIKON, NA ¼ 0:30, workingdistance WD ¼ 7:4mm), 20× (NA ¼ 0:40, WD ¼4:7mm, and 50× (NA ¼ 0:55, WD ¼ 0:34) are 20mm,10mm, and 4mm, respectively. The field of view of10×, 20×, and 50× Mirau-interferometric objectivesare 2mm, 1mm, and 0:22mm using a 20mm dia-meter eyepiece and 0:88 × 0:66, 0:44 × 0:33, and0:18 × 0:13mm2 using a 2=3 inch sensor. The theore-tically calculated transverse resolution for 10×, 20×,and 50× Mirau-interferometric objectives is 1.29,0.96, and 0:7 μm, respectively. The lateral resolution0:7 μm of the present system is very high comparedto conventional OCT systems and OCM-basedMichelson interferometric objective lenses. Further,the present system is totally nonmechanical scan-ning, common path geometry, compact, and it usessingle objective lens as compared to OCMs based onMichelson and Linnik-type interferometric config-urations. Therefore the phase stability of the presentsystem is expected to be high.
3. Experimental Details of the Mirau InterferometerBased FF-OCM
A schematic diagram of the FF-OCM based on theMirau interferometer is illustrated in Fig. 1. In thisexperimental system, the same swept source is usedas discussed by Dubey et al. [10]. The swept-sourcesystem is built by combination of a broad band lightsource SLD (Model No. SLD-371-HP1-DIL-PM-PD,SUPERLUM Diodes Ltd., FWHM of Δλ ¼ 48:38nmand center wavelength λ0 ¼ 842:5nm, output power¼ 7mW) and an electronically controlled AOTF(NEOS Technologies, Inc., USA, line width δλ ¼1:5nm), which is connected through a single-modefiber by a fiber connector. The output power of theAOTF is about 200 μW. The swept source is madeto incident on the Mirau objective installed on thereflection vertical microscope (NIKON ECLIPSE
50i, Japan). The output light passes through themicroscopic device and is redirected by a beam split-ter (BS1) toward the Mirau objective and reaches an-otherbeamsplitter (BS2). Thebeamispartly reflectedby BS2 toward the reference mirror, and the trans-mitted beam is made incident onto the object surface.The two beams, one reflected by the reference mirrorand the other by the object surface, is recombined atBS2 and further passes through the objective lens. Arelay lens is used to image the object onto the CCDimage sensor.
The biological sample was placed on the objectstage, and one can obtain the interference fringesignal within the maximum imaging depth range,which can be calculated by [3,16] Zmax ¼λ20=4ðδλsÞnavg. At the wavelength sampling interval(δλs ¼ δλsampling ¼ 0:75nm), the maximum imagingdepth of the present system is about 175 μm. Further,the instantaneous coherence length of the filteredlight can be calculated by Lc ¼ 4 ln 2λ20=navgπδλ andcomes out to be 309 μm [2,3] Now, radio frequency(RF) to the AOTF was tuned sequentially with aconstant step of 0:1MHz from 87 to 95MHz(810–870nm). The corresponding shift in the peakof the tuned wavelength was observed to be∼0:75nm. Therefore, for every 0:1MHz shift in theinput frequency, the peak of the tuned spectrumwas shifted by 0:75nm. This is the wavelength sam-pling interval (δλs) of the present system. As theAOTF exhibits a linear relationship between thewavelength and RF, the line width of the tuned spec-trum remains the same as 1:5nm, which is the band-width of the AOTF, throughout the sweeping width of
0:75nm multiplied with 81 tuning steps, whichequals 60:75nm. These 81 tuning steps generated81 interferograms, which are recorded by a CCD de-tector (Roper Scientific, Inc.). The parameters of thiscamera are: image format, 1392 × 1024 pixels; pixelsize, 4:65 μm × 4:65 μm; frame rate, 10 frames persecond (fps); and exposure time, variable in the rangeof 0.1–0:2 s. Recorded interferograms were thananalyzed by an algorithm written in MATLAB.
The axial and transverse resolution were deter-mined experimentally. For the axial resolution thecoherence properties of the SLD light was measuredwith the same interferometric microscope using 50×Mirau objectives. A reflective mirror was used in-stead of a sample and whose position was scannedaxially such that the coherence function could bemeasured directly. The result is shown in Fig. 2(a),and the measured value was found to be 3:8 μm forthe axial resolution which is close to the theoreticallyobtained value (2:5 μm). To determine the transverseresolution of the present system, 1 μm diameter poly-styrene beads were imaged. The image of each beadin the CCD camera represents the point-spread func-tion (PSF) of the microscope, which is measured bythe 50× Mirau objectives. The PSF in the X-directionis shown in Fig. 2(b), from which, the FWHM trans-verse resolution measured was 1:2 μm. It is close tothe theoretical value of 0:7 μm. The transverse reso-lution was also tested by using an United States AirForce (USAF) target. It can be seen from Fig. 2(c)that the present system could resolve the imagesof elements 2 and 4 using 10× (spatial period of25 μm), and Fig. 2(d) shows the well-resolved image
Fig. 2. (a) Axial and (b) transverse resolution (c) imaging of USAF target using 10×, and (d) imaging of USAF target using 50×.
of element 1 and corresponding bars using 50× mag-nification (spatial period of ¼ 8 μm) in the USAFresolution target next to the smallest bar.
4. Results and Discussion
To test the performance of the experimental setup,the Mirau objective with magnification of 10× and20× was used for imaging onion skin. The experimen-tal results presented in this paper are cross-sectionalamplitude and phase images of onion skin using 20×Mirau objectives. The 20× objective provides a suffi-cient field of view and required transverse resolutionfor imaging of onion cells. The onion skin sample wasprepared and placed on the aluminum-coated glassslide held in a XYZ translational stage. The onionskin is nonuniform due to different thicknesses ofthe cell wall and cell structure at different positions.Therefore, the OPD is also different at each position.By sweeping the RF, 81 spectral interferogramimages were recorded at different wavelengths andthen stacked as Iðx; y; kmÞ. The stacked interfero-grams were then analyzed using an algorithm devel-oped in MATLAB, as similarly described by Sarunicet al. [8].
Figure 3(a) shows the example of an interferogramrecorded at a wavelength of 843:7nm (RF 91MHz).Interferograms for the entire tuned spectrum werestacked together along the wavelength axis, andthe corresponding variation of intensity along thewavelength axis was computed for a fixed lateral po-sition of the interferograms. The spectral interfero-gram can be seen in Fig. 3(b), which shows thevariation of spectral intensity for recorded interfero-grams along the wavelength axis. A fast Fouriertransform (FFT) of the interference fringe signal
was computed, which provides multiple peakscorresponding to different depth layers of the objectshown in Fig. 3(c). By means of selective filtering ofFourier peaks, the amplitude (cross-sectional imagesat different depths) images were obtained. A FFT ofthe stacked interference signal information can beconverted into depth information by knowing theaverage refractive index of the object as shown inFig. 3(d). The depth of the layer was determined byassuming an average refractive index of 1.35. Eachmultiple peak of Fig. 3(c) (X-axis is in frequencycycles per second [Freq. c/s]) corresponds to differentdepth layers of the object, which are shown inFig. 3(d), and where the X axis shows the depth inmicrometers. Therefore, the cross-sectional depthprofile of the sample were reconstructed by eliminat-ing its conjugate mirror image. The enface image ofthe onion skin was then reconstructed by iteratingthese procedures for every detector pixel, as shownin Figs. 4(a)–4(d) for axial positions at 29, 33, 57,and 65 μm, respectively. In Fig. 4(a) only the cellstructure is visible but not the complete structureof the onion skin. The best optically sectioned imagewas obtained at 33 μm, as can be seen from Fig. 4(b).In Fig. 4(b) all structural information, such as insidethe cell (epithelium) and cell wall, are clearly visible.At a higher depth of 57 μm [Fig. 4(c)], the lower cellstructure is visible but the cell walls are not visible.At 65 μm [Fig. 4(d)], only the cell walls are promi-nently reconstructed but the cell structure is not visi-ble. Corresponding to Figs. 4(a)–4(d), the wrappedphase maps were also computed which are shownin Figs. 4(e)–4(h), respectively. The unwrapped phaseimage is obtained at the best optically sectioned im-age position of 33 μm and its three-dimensional (3D)
Fig. 3. (Color online) (a) Interferogram at 843:7nm (RF 91MHz), (b) variation of intensity for recorded interferograms along the wave-length axis, (c) FFT of the interference signal for the stacked interferograms, (d) FFT of the interference fringe signal corresponding todepth (micrometers).
topography is shown in Fig. 4(i), in which the phase isin radian. The image volume of the recordedinterference fringe pattern is 3236:4 μm× 2418 μm ×175 μm ðX :Y:ZÞ, but to reduce the image reconstruc-tion time we have cropped the central part of the
image, and the image volume of the onion skinis 1395 μm × 1627:5 μm × 175 μm.
Further, the system was used for the quantitativeimaging of human blood cells using a 50× Mirau ob-jective to achieve a higher transverse resolution than
Fig. 4. (Color online) (a)–(d) Cross-sectional images of the onion skin at 29, 33, 57, and 65 μm depth, respectively, (e)–(h) correspondingphase map of (a)–(d), and (i) unwrapped phase map at 33 μm.
a 20× objective. A blood sample was collected fromthe hospital and was diluted (1 drop of blood in1:5ml of saline water, a standard protocol followedby pathologists). The solution was sandwiched be-tween the transparent cover slip (upper part) andthe aluminum coated cover slip (lower part) and im-aged. When the blood sample was on a static state, bysweeping the wavelength of the light source, 81 spec-tral interferograms were captured which encode theamplitude information of red blood cells (RBCs)along the sample depth. A 2D spatial interferogramimage of the RBCs at 843:7nm (RF 91MHz) isshown in Fig. 5(a). Figures 5(b)–5(e) show thecross-sectional images of the static RBC at differentdepths (16, 31.2, 32.9, and 65 μm, respectively).Figure 5(b) is very near to the DC component, andonly the top view of the blood cells is visible butthe detailed features are not clear. From higher orderpeaks, the images of RBCs are shown in Figs. 5(c)and 5(d). It can be seen from Fig. 5(c) that the shapeof the RBCs is very clear but the quality of the imagewas not good. At a depth of 32:9 μm, the image of theRBC is best reconstructed with the boundary of theRBCs sharply visible. However, at a depth of 65 μm,as shown in Fig. 5(e), the shape of the blood cell is notproper reconstructed. The corresponding wrapped
phase maps are shown in Figs. 5(f)–5(i). The un-wrapped phase image was obtained at a depth of32:9 μm, and its 3D topography is shown in Fig. 5(j)with the height unit in micrometers. The correspond-ing refractive index profile is shown in Fig. 5(k) for aline across the big cell. From this refractive indexprofile, the average value of the refractive index iscalculated as about 1.4345.
For computing the optical signal-to-noise ratio(OSNR) for the present system, the expression can
be given by OSNR ¼ 10dB: log10�SN
�, where S repre-
sents the optical signal power, and N is the opticalnoise power [2]. For the multiple detectors (CCDarrays, M ×M pixels), the signal-to-noise ratio canbe expressed by [2] ðSNÞ ≈ ðηPsT
hυ Þ1=2, where Ps is the op-tical power received by the detector, υ is the fre-quency of the light, η is the detector quantumefficiency, h is the plank constant, and T is the acqui-sition time. In the present case Ps ¼ 200 μW,υ ¼ c
λ0 ¼3×108 m=s842:5nm , η ¼ 30% at 842:5nm, h ¼
6:6 × 10−34 j=s, and T ≈ 0:1 s. Therefore for the pres-ent system the calculated OSNR is about 67dB.
From the FF-OCM we were able to observe enfaceOCM images of an onion and RBCs at different
Fig. 5. (Color online) (a) Interferogram at 843:7nm (RF 91MHz), (b)–(e) cross-sectional images at 16, 31.2, 32.9, and 65 μm depth,respectively (f)–(i) corresponding wrapped phase map of (b)–(e), (j) unwrapped phase map at 32:9 μm, and (k) refractive index profile.
depths. Further, we were also able to reconstruct thephase maps of both the RBC and onion skin, and thisinformation may be important for quantitative eva-luation of biological cells such as refractive index,height distribution, etc. But the main shortcomingof our system is the long time for recording and re-construction. In the present case, the param-eters of the CCD camera used are image format:1392 × 1024 pixels, pixel size: 4:65 μm × 4:65 μm,frame rate: 10 fps, and exposure time: variable inthe range of 0.1–0:2 s. Thus recording of the raw datatakes approximately 8 s and postprocessing to recon-struct the images takes about 2 min. This situationcan be improved by using better hardware andsoftware.
5. Conclusion
In the present paper the quantitative imaging of bio-logical cells using a common path high-resolutionFF-OCM is demonstrated. The FF-OCM is realizedby using a swept-source system (SLD and AOTF),Mirau interferometer, and CCD camera. The inter-ferometric signal generated by the Mirau microscopeobjective was analyzed by a Fourier analysis. Opti-cally sectioned images and a quantitative phasemap of biological cells, such as onion skin and RBCs,show that with a 50× Mirau objective, 3:8 μm axial,and 1:2 μm transverse resolution can be achievedwithout X , Y mechanical scanning. Because the sys-tem is implemented in a common path geometry, it ismore stable and less sensitive to external perturba-tions. In addition to that, the present system usesparallel detection, measures enface images, and usessingle objective lens as compared to OCMs based onMichelson and Linnik-type interferometric objectivelenses, therefore the phase stability of the presentsystem is expected to be high.
The authors gratefully acknowledge the financialassistance from the Department of Science and Tech-nology, Delhi, Government of India for the project SR/S2/LOP-0021/2008 and Mr. Fool Chand Saini work-ing in the pathology lab at the Indian Institute ofTechnology Hospital for providing the blood samples.
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