Axial-Lateral Parallel Time Domain OCT

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1. IntroductionOptical coherence tomography (OCT) is a noninvasive, noncontact imaging modality used toobtain high-resolution cross-sectional images of tissue microstructure [1]. Conventional timedomain (TD)-OCT can detect the echo time delays of light by measuring the interferencesignal as a function of time during axial scanning in a reference arm at each position of aprobe beam scanning the sample arm laterally. Imaging sensitivity decreases when fasteraxial scanning is applied to increase frame rate [2]. Fourier domain OCT (FD-OCT) canallow higher sensitivity and imaging speed than TD-OCT [3–6]. FD-OCT uses either aspectrograph [4] or a frequency swept laser source [5] to measure the echo time delays of light by spectrally resolving the interference signal without axial scanning.

A parallel detection spectral domain (SD)-OCT technique has been developed to obtaincross-sectional images from a single captured image without axial and lateral scanning [7–10]. More recently, this technique has applied linear illumination and a two-dimensional (2-

D) charge-coupled device (CCD) camera to measure three-dimensional (3-D) shapes [8], invivo real-time imaging of human eye structures [9], and in vivo 3-D dermatologicalinvestigations [10]. OCT images require mapping and interpolating the axial data fromwavelength- to k-space and subsequent application of the Fourier transformation. FD-OCT isknown to contain DC and conjugate artifacts and to suffer from a strong fall-off of SNR,which is proportional to the distance from zero delay and a sinc-type reduction of depth-dependent sensitivity because of limited detection line width. To avoid artifacts, SD-OCTrequires several phase-shifted spectral interference signals [11,12]. For in vivo imaging of biological samples, the accuracy of phase differences between captured frames did not proveto be promising due to sample motion.

Parallel detection TD-OCT techniques have been developed to obtain transverse ( en face )[13–17] and longitudinal [18–20] cross-sectional images. TD-OCT images, which arecalculated using interference images, avoid the standard FD-OCT problems of mirror imagesand decreased SNR with increasing depth range. As full-field (FF) OCT can measure en face images [13–17], this scheme requires an axial mechanical scan to obtain longitudinal cross-sectional images. To obtain a depth-resolved interference image of a sample during exposureby a 2-D camera, the axial–lateral parallel (ALP) detection scheme uses 1 st order diffractedlight as a reference beam to generate a continuous spatial optical delay, and a linearillumination light as a probe beam [18]. Using a three-step phase-shifting method, wedemonstrated in vivo OCT imaging at 10 fps using an indium gallium arsenide (InGaAs)

#80091 - $15.00 USD Received 13 Feb 2007; revised 9 Apr 2007; accepted 11 Apr 2007; published 13 Apr 2007

(C) 2007 OSA 16 Apr 2007 / Vol. 15, No. 8 / OPTICS EXPRESS 5209



digital camera operating at 30 fps [19]. We were able to obtain OCT images of human fingerswith a 90-dB sensitivity for a 4.80 × 2.45-mm 2 (lateral × axial) imaging range. Using anultrahigh-speed complementary metal oxide semiconductor (CMOS) camera, we obtainedOCT images (512 × 512 pixels) with a 5.8 × 2.0-mm 2 (lateral × axial) imaging range at 1500fps by calculating two sequential images [20]. Lateral and axial ranges were fixed by theimaging lens and the Littrow angle at 1 st order diffracted light.

In this paper, we demonstrate a method of adjusting the imaging range in ALP TD-OCTusing an optical zoom lens and high-order diffracted lights. Our method allows the lateralrange to zoom continuously from 4 to 8 mm using an optical zoom lens. Although zoomingdecreases the axial range, this can be recovered using higher-order diffracted lights. Becausediffraction grating is only used for the reference beam, the low-diffraction efficiency of high-order diffracted light is sufficient to generate the reference beam. The system yields 94.6-dBsensitivity with a 1.05-ms InGaAs camera exposure and can display OCT images (320 × 256pixels) of the human finger in vivo at 30 fps.

2. Experimental setup

Figure 1 presents a schematic of the ALP TD-OCT system. The collimated light of asuperluminescent diode (Qphotonics, SLD QSDM-1300-9; center wavelength: λ 0 = 1.31 μm,full-width at half-maximum spectral width: Δ λ = 30 nm, coherence length: lc = 50.3 μm) issplit into sample and reference arms by a non-polarizing cube beam splitter (20 mm in size).

A cylindrical lens ( f = 50 mm) was inserted in the sample arm to illuminate the sample with alinear beam. A reflective diffraction grating was installed in the reference arm with a Littrowconfiguration. The grating equation is given by

( ) λ β α n p =+ sinsin , (1)

where p is the spacing between grooves, 1/300 mm; λ is diffracted wavelength; α and β areincident and diffraction angles, respectively; and n is the order of diffraction. Since theincident angle is equal to the diffraction angle in the Littrow configuration, the Littrow angleθ is determined by

( ) pn 2sin 01 λ θ −= . (2)

Although the center wavelength beam propagates backward along the incoming path, thediffractive angles of other wavelengths λ can be described as

( )θ λ β sinsin 1 −= − pn . (3)

Backscattered light from samples and diffracted light from the grating were imaged onto anInGaAs camera (Goodrich-Sensors Unlimited Inc., SU320MS-1.7RT; 256 (H) × 320 (V)pixels, 25- μm pixel pitch, active area of 6.4 × 8.0 mm, 12-bit resolution, frame rate of 60 fps)using an optical zoom lens (Edmund Optics, VZM 200i, Parfocal Zoom: 0.5–2 ×, workingdistance: 90 mm). We used the camera’s horizontal pixels ( N = 256) and vertical pixels ( M =320) to measure axial and lateral ranges in samples, respectively. Imaging depth, Δ Z ,generated by the diffraction grating, is given by

θ tand Z =Δ , (4)

where d is the beam diameter. Since the lateral range, Δ X , is measured by the camera’svertical pixel, horizontal range Δ Y corresponds to N Δ X / M . Therefore, the relationshipbetween Δ Z and Δ X can be described as

θ θ tantan X M N

Y Z Δ=Δ=Δ . (5)





According to the sampling theorem, when an axial profile, Δ l, is sampled by two pixels, themaximum imaging depth range in air, Δ Z max, can be described as

222max N l N

l Z c ×=×Δ=Δ . (6)

Because lc = 50.3 μm and N = 256, Δ Z max = 3.2 mm in our system. If the actual imaging

depth of the camera is greater thanΔ

Z max, the axial resolution depends on the imaging depthand the number of pixels. The axial–lateral interference image, I , is described as

( )[ ] φ γ cos)(),(2),(21

z z x R I I I I z x I siginref ref sig ++= , (7)

where I sig , I ref , and I in are the intensities of the sample beam, reference beam, and incidentbeam, respectively; Rsig is the distribution of the sample reflectance; γ ( z) is the amplitude of the modulation, which is determined by the light source’s degree of coherence; φ is the phasedifference between sample and reference beams; and * denotes the convolution operator.

Fig. 1. Schematic of axial–lateral parallel time-domain optical coherence tomography. SLD:

superluminescent diode, BS: beam splitter, CL: cylindrical lens. Inset is the camera area. Thehorizontal pixels ( N = 256) and vertical pixels ( M = 320) were used to measure axial andlateral ranges in samples, respectively.

Since the camera output contains a noninterference signal, the amplitude of theinterference signal, and a phase term, producing an OCT image requires more than threephase-shifted interference images. High-speed imaging requires obtaining OCT images of biological tissues in vivo due to sample motion. Noninterference light is much stronger thanthe interference signal for imaging biological samples. Therefore, it is very important toeliminate noninterference components using a minimal number of frames. When the phasedifference between the two interference images is generated by moving a sample, the squaredvalue, S, of the difference between two captured images ( I 1 and I 2) can be calculated as

( ) ( )[ ]( )2212

21 coscos)(),(4 φ φ γ −=−= z z x R I I I I S siginref . (8)

Although the calculated results include the phase term, residual fringes are not visible becauseOCT images of biological samples contain speckle noise. Therefore, the calculated image S represents the distribution of the sample reflectance Rsig( x, z) that corresponds to an OCTimage, although it contains noise. The image averaging procedure is a powerful way of reducing the phase and speckle noise [15,16,18]. Since the calculation is simple, the OCT





images can be displayed at 30 fps using homemade software. We used the averagingprocedure to reduce this noise using OCT images stored in a personal computer.

3. Results and discussions

3.1 Calculation of measurement range at each order of diffraction

First, we calculated the Littrow angle at each order using Eq. (2), as shown in Table 1. As the

light source has spectral width, diffracted light is widespread. Figure 2 shows the diffractionangle β calculated using Eq. (3) and the spectrum of SLD used. At the 5 th order, diffractedlight is not generated at longer wavelengths, so the diffracted light from the 1 st to 4 th order canbe applied to the reference beam. Furthermore, the measured diffraction efficiencies from the1st to 4 th orders are also shown in Table 1 when the reflectance of the plane mirror is 100%.The measured diffraction efficiencies are less than 20% and sufficient for use as referencebeams.

Table 1. Littrow angle at each order diffracted light.

1st order 2 nd order 3 rd order 4 th order 5 th orderLittrow angle (deg.) 11.33 23.14 36.12 51.87 79.27Diffractionefficiency (%) 14.5 10.5 9.2 5.9

Fig. 2. Calculated diffraction angles at each order and spectrum of SLD

Next, we estimated axial and lateral ranges in our system. When the optical zoom lens is setat a 1.0 × magnification, lateral range Δ X corresponds to the horizontal size of the active area(8 mm) in the camera. Lateral ranges vary from 16 to 4 mm for magnifications of 0.5 to 2 ×.Figure 3(a) presents the calculated lateral range and axial range Δ Z at each order of diffractedlight; at the 4 th order, the axial range is similar to the lateral range. While the axial range at4th order diffracted light is greater than maximum value Δ Z max = 3.2 mm, it can be effectivefor measuring OCT images if the lateral range is set below 3.2 mm by increasingmagnification.

The axial resolution is not affected by the dispersion of the diffraction grating if the gratingplane is optically conjugated with the plane of the camera. Therefore, the axial resolutiondoes not depend on the diffraction order of the grating. However, the axial resolutiondecreases and depends on the axial range and the number of pixels in the axial direction if theaxial range exceeds the maximum imaging depth. We estimated the axial resolution in airusing Fig. 3(a) and Eq. (6), as shown in Fig. 3(b). Here, the axial resolution is half thecoherence length of the light source when the axial range is smaller than the maximum depth.When the magnification is below 1.0 ×, the illumination intensity of the samples is too weak for efficient imaging of biological tissue due to the large illumination size. For this reason,we selected a magnification range from 1.0 to 2.0 × for taking practical measurements.





Fig. 3. (a) Calculated imaging ranges at each order of diffraction. Solid lines represent axialrange. Broken lines represent lateral range. (b) Estimated axial resolutions in air at each orderof diffraction.

3.2 Lateral resolutions

We investigated the smallest resolvable element in a test target (USAF1951) while increasingthe optical zoom lens magnification. Increased lateral resolution can be obtained bycompromising the lateral range. Figure 4(a) presents a line profile of group 3 at 1.0 ×

magnification. Test target contrast was 31% at group 3 element 5 (12.7 line pairs/mm),corresponding to a resolution of about 78.7 µm. Figure 4(b) presents a line profile of group 5at 2.0 × magnification. Although the smallest resolvable element was 40.3-line pairs/mm(group 5 element 3), corresponding to a resolution of about 24.8 µm, this was lower than the88-line pairs/mm resolution specified by the manufacturer. As the zoom lens was designed touse visible light and its wavelength was intended for a silicon CCD camera (e.g., 640 × 480pixels), the longer near-infrared wavelengths and a smaller number of pixels result indecreased resolution. Since the camera resolution was twice the pixel pitch (25 μm) and theoptical zoom lens used a 2.0 × magnification, the resolution of the optical system wasestimated to be 25 μm, corresponding to the measured resolution. For actual measurementsof biological tissues, the lateral resolution could be decreased as a consequence of coherentcross talk because of the high spatial coherence light used and the degradation resulting frommultiple scattering deep in biological tissues.

Fig. 4. (a) Measured line profile of group 3 at 1.0 × magnification. (b) Measured line profile of

group 5 at 2.0 × magnification

3.3 Beam width of linear probe beam

To investigate the influence of aberrations in the cylindrical lens used, we measured beamwidth (1/e 2) in the focusing direction of the probe beam by moving a beam profiler (Coherent,





Beam Master) axially in 100- μm steps, as shown in Fig. 5(a). The normalized profile of aGaussian beam is described as

( )[ ]( ) ( )

−= z

r

z zr I in 2

2

22

exp2

,ω ω

π ω . (9)

Here, the beam radius,ω

( z

), is described as

( ) ( )

+=22

002

02 1 πω λ ω ω z z , (10)

where the waist diameter is 2 ω 0 = (4 λ 0 / π )( f / d ). Our experimental results were similar to thetheoretical curves for an expected incident beam diameter of d = 6.5 mm. The measuredbeam width at the waist was 27.3 μm, greater than the calculated value of 12.8 μm, due toaberrations in the cylindrical lens. The measured depth of focus was about 600 μm, threetimes greater than the calculated 197 μm.

The peak intensity ratio of focused beam to incident beam on the beam axis ( r = 0) isexpressed as

( )[ ]

( ) ( )=

z

d

d I

z I

in

in

ω

ω

22 / ,0

,0(11)

Figure 5(b) shows the peak intensity ratios of the focused beam to the incident beam usinga logarithmic scale. The intensity ratio peaked at 23.8 dB at the beam waist and droppedgradually with increasing z, indicating that this focusing allowed our system to gain more than15 dB.

Fig. 5. (a) Measured linear beam widths. Solid lines represent theoretical curves. (b) Peak intensity ratios of focused beams to the incident beam.

3.4 Sensitivity

We measured the sensitivity of our OCT system by increasing the magnification. A planemirror was used as a sample with an attenuation of 50 dB. This plane mirror was oscillatedusing a piezoelectric transducer to provide a 180º phase difference between two sequentialinterference images. The total illumination power used was about 6.6 mW, corresponding to20.6 µW optical power per A-line (6.6 mW divided by the camera’s 320 pixels) with acamera exposure time of 1.05 ms. We used a neutral density (ND) filter to adjust the opticalpower of the reference beam until pixel values were similar to the camera’s saturation level ata 1.0 × magnification. Figure 6 presents the pixel values of the captured interference imagesand sensitivities when we increased the magnification. Because pixel values decreased withincreased magnification, the resultant sensitivities decreased from 94.6 to 86.0 dB. Theincident power must be adjusted to achieve constant sensitivity in the zoom range.





We estimated the theoretical sensitivity of ALP TD-OCT using values for FF-OCT, whichcalculates two interference images [16]. Assuming measurements are limited by shot-noise,the minimum detectable reflectivity, Rmin, without image accumulation is approximately

( )max

2

min 2 ξ ref

incref

R

R R R

+= , (12)

where Rref , is reference reflectivity, ξ max is the camera’s full-well capacity, and Rinc is thereflectivity of incoherent light. Our InGaAs camera has a large full-well capacity, ξ max ≈ 8 ×105. The reference reflectivity was determined by the optical density used in the ND filterand the diffraction efficiency in the reference arm. We measured reference reflectivity to be

Rref = 2.5% when the reflectivity of a plane mirror was measured at Rref = 100%. Theincoherent component of signal lights was negligible when a plane mirror was used as thesample. Therefore, these values gave a predicted sensitivity of 10log( Rmin) ~ –78.1 dB. In theFF-OCT scheme, which uses microscope objectives in both arms, the sample has anillumination area equal to that of the reference. In ALP TD-OCT, optical density at thesample is greater than at the reference because the cylindrical lens focuses the probe beamlinearly. Considering the 23.8 dB gain in the sample arm of our system, the theoreticalsensitivity is reached at 101.9 dB. The measured sensitivity in our system was approximately7 dB lower than the theoretical estimate due to electrical noise from the InGaAs camera.

Fig. 6. (a) Pixel values and (b) sensitivities with an attenuation of –50 dB in the sample arm for

each magnification.

3.2 In vivo OCT imaging of human fingers

We conducted in vivo OCT imaging of human fingers at 1.0 and 2.0 × magnifications usingthe 2 nd order of the diffracted light as a reference beam. The incident power used was about0.8 mW with a 1.05-ms camera exposure time. We averaged 30 OCT images, which werecalculated using two sequential interference images to reduce speckle noise, and the averagedOCT images were presented on an inverse logarithmic scale. Figure 7(a) shows an OCTimage of a human nail fold region at 1.0 × magnification. The imaged area (lateral × axial)was 8.0 × 2.6 mm 2. The nail root is visible beneath the skin. The lunula, which is thewhitish, half-moon shape, can be seen at the nail base underneath the plate. Figure 7(b)shows an OCT image at the same position when magnification was increased to 2.0 ×. Theimaged area (lateral × axial) here was 4.0 × 1.3 mm 2. The size of this OCT image wasreduced to 50% and then overlapped with Fig. 7(a), as shown in Fig. 7(c). The OCT image at2.0× magnification, displayed as the gray region, agrees with the OCT image at 1.0 × magnification.





Fig. 7. In vivo OCT images of a human nail fold region (a) at 1.0 × magnification, with animaging range of 8.0 × 2.6 mm 2 ( x × z); (b) at 2.0 × magnification, with an imaging range of 4.0× 1.3 mm 2 ( x × z); and (c) with images overlapped, where the gray region corresponds to Fig.7(b).

Since the axial range decreased when we increased magnification of the optical zoom lens,we used high-order diffracted lights to recover the axial range. Figure 8 presents in vivo OCTimages of a human nail fold region at a 2.0 × magnification using 2 nd, 3 rd, and 4 th orders of diffracted lights; axial ranges were 1.3, 2.3, and 4.1 mm, respectively. These images wereresized to imaging range. Figure 9 presents axial profiles of the nail plate at each image (redline). Here, the position at the nail surface was set to zero. At the 4 th order, the axial profileof the nail plate surface was broad because the maximum axial range (3.2 mm) had beenexceeded. According to Fig. 3(b), the axial resolution in air is about 32 µm at the 4 th order of diffraction and 2 × magnification. Therefore, a 3 rd order of diffracted light is suitable for useof the reference beam.

Fig. 8. In vivo OCT images of a human nail fold region at (a) 2 nd, (b) 3 rd, and (c) 4 th orders of diffracted light. Axial ranges were 1.3 mm, 2.3 mm, and 4.1 mm, respectively. The red linescorrespond to the region of axial profiles in Fig. 9.

Fig. 9. Axial profiles of the nail plate in each OCT image





4. Conclusion

We demonstrated the adjustment method for ALP TD-OCT using an optical zoom lens andhigh-order diffracted lights for a variable imaging range. When the lateral range was adjustedfrom 8 to 4 mm using an optical zoom lens, the resultant lateral resolution improved from 78to 25 µm. The reduced axial range was recovered by using higher-order diffracted lights.Since the InGaAs camera used only had 256 × 320 pixels at 60 fps, this low number of pixels

limited lateral resolution and axial range, and the frame rate limited the time resolution of OCT images. These limitations could be diminished by using a commercially available high-performance InGaAs camera (SU640SDWH-1.7RT: 512 × 640 pixels, 109 fps). Our ALPTD-OCT system is artifact-free, sufficiently sensitive (94.6 dB) to image biological tissue,and can display OCT images in real time because it uses only simple calculations. In addition,its adjustable range can be useful for OCT imaging in a diverse range of fields.

Acknowledgments

This study was supported by Industrial Technology Research Grant Program in ’05 from NewEnergy and Industrial Technology Development Organization (NEDO) of Japan.



Axial-Lateral Parallel Time Domain OCT

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