Optical Coherence Tomography for Medical Imaging Overview

White PaperSPRABB9–June 2010

Signal Processing Overview of Optical CoherenceTomography Systems for Medical Imaging

Murtaza Ali and Renuka Parlapalli ......................................................................................................

Optical Coherence Tomography (OCT) is a new medical imaging modality with resolution in the µm rangeand depth of imaging in the mm range. OCT is based on the principle of low coherence interferometry.This modality has been applied to imaging in various biological applications including ophthalmology,gastroenterology, dentistry, cardiology, tumor margining, etc. OCT systems are signal processing intensiveand well suited for embedded implementations using digital signal processors (DSP) and system-on-chip(SoC) application processors. Low-power DSP and SoC are key to making low cost, low power andportable OCT systems. The different types of OCT systems are described in this white paper with focusbeing on signal processing algorithms used in such systems.

Contents1 Introduction .................................................................................................................. 22 OCT Systems ................................................................................................................ 33 Basic Signal Processing Chain in OCT Systems ....................................................................... 94 Advanced Signal Processing in OCT Systems ........................................................................ 125 DSP for OCT Signal Processing ........................................................................................ 186 Conclusion .................................................................................................................. 187 References ................................................................................................................. 198 Acknowledgement ......................................................................................................... 21

List of Figures

1 Schematic of OCT System Based on Michelson Interferometer...................................................... 3

2 Schematic of Time Domain OCT System................................................................................ 4

3 Example of Received Signals With Two Reflecting Surface .......................................................... 5

4 Schematic of Spectral Domain OCT System............................................................................ 6

5 Example of Received Interference Signal Captured on an Array Detector.......................................... 7

6 Schematic of Swept Source OCT System ............................................................................... 8

7 Image Formation Path .................................................................................................... 10

8 Representation of Signals in the Signal Chain ........................................................................ 10

9 Dispersion Compensation per Wojtkowski et al. ..................................................................... 12

10 Dispersion Compensation per Marks et al. ............................................................................ 12

11 Doppler Imaging Signal Chain Using Kasai Algorithm for OCT Systems .......................................... 13

12 Example of a Polarization Sensitive OCT System Using Two Line Scan Camera ............................... 15

13 Signal Processing Chain in Polarization Sensitive Spectral Domain OCT......................................... 16

14 Spectroscopic Data Generation in Frequency Domain OCT ........................................................ 17

15 Spectroscopic Data Generation in Frequency Domain OCT With Frequency Domain Windowing ............ 17

List of Tables

1SPRABB9–June 2010 Signal Processing Overview of Optical Coherence Tomography Systems forMedical Imaging

Copyright © 2010, Texas Instruments Incorporated

Introduction www.ti.com

1 Introduction

OCT is a new medical imaging modality with resolution in the µm range and depth of imaging in the mmrange [3], [8], [10], [28]. OCT uses the principle of low coherence interferometry to perform a depthresolved axial scan. By stacking the axial scans in X and/or Y directions, two or three dimensional imagingis feasible.

OCT can be used to image various aspects of biological tissues. Some of these include:

• Structural information: This is the most typical OCT imaging. It measures the local reflectivity of thetissue.

• Blood flow: Using Doppler technique, the blood flow in tissues and vessels can be estimated.• Polarization sensitive: The change of polarization states through tissues can be estimated.• Elastography: The elastic parameters of the tissue can be estimated.• Spectroscopy: The variation of absorption, reflectivity and scattering with wavelength can be measured

providing clues to molecular content of the tissue.

Any combination of the above imaging modes can be used to bring out specific features of biologicaltissues as desired.

Applications of OCT in various biomedical imaging applications include:

• Ophthalmology: Very fine imaging of the retina with capability to identify several eye diseases ispossible with OCT. Most of the commercial products available today are for ophthalmologic usage.

• Dermatology: To image subsurface structural and blood flow information.• Dentistry: To image structure of teeth and gum line at the same time to visualize bacteria in concert

with the tooth and roots.• Gastroenterology: To image the gastrointestinal (GI) tract through endoscopic probes.• Intra-vascular: To image plaques inside blood vessels.• Cancer diagnosis: Several modes in OCT imaging can discriminate between malignant and normal

tissues allowing cancer diagnosis through either non-invasive or minimally invasive procedures.• Intra surgery for tumor margining: Enables discrimination between malignant and non-malignant tissue

to decide the regions of tissue to be removed during surgery.

OCT systems are signal processing intensive. The need for acquiring real-time data, processing theacquired data to extract meaningful information and then displaying the information in a clinically relevantway is well suited for embedded implementations using DSP and SoC application processors. The adventof low-power DSP and SoC is an added benefit for OEMs to develop low cost, low power and evenportable systems based on OCT technologies without compromising the image quality needed for clinicalapplications. In addition, the programmability and scalability of these devices allow optimizing the signalchains for different applications on the same platform.

This white paper concentrates on various signal processing algorithms used in OCT systems. Section 2introduces three types of commonly used OCT techniques: time domain, spectral domain and sweptsource-based OCT. The latter two techniques are more popular due to their fast acquisition time,therefore, focus is on these systems in the rest of the paper. Section 3 describes the signal processingsteps needed to form the image from the raw data. Section 4 describes the additional signal processingalgorithms needed for different variations of OCT systems, e.g., in Doppler or polarization-based systems.

C64x+, TMS320C64x+ are trademarks of Texas Instruments.All other trademarks are the property of their respective owners.

2 Signal Processing Overview of Optical Coherence Tomography Systems for SPRABB9–June 2010Medical Imaging


Source

Photo Detector

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www.ti.com OCT Systems

2 OCT Systems

OCT uses a standard Michelson Interferometer with a low-coherence light source as shown in Figure 1. Inthe interferometer, the incoming broadband beam of light is split into the reference path and the samplepath which are recombined after back-reflection from the reference mirror and the multiple layers of thesample, respectively, to form an interference signal. The broadband nature of light causes interference ofthe optical fields to occur only when the path lengths of the reference and the sample arm are matched towithin the coherence length of the light. This interference signal carries information about the sample at adepth determined by the reference path length.

Figure 1. Schematic of OCT System Based on Michelson Interferometer

These systems can be broadly classified into:

• Time domain (TD) OCT systems• Spectral domain (SD) OCT systems• Swept source (SS) OCT systems



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2.1 Time Domain Systems (TD-OCT)

TD-OCT systems are the conventional, first generation OCT systems. In TD-OCT, an interference patternis obtained by moving the reference mirror in a linear fashion to change the reference path length andmatch multiple optical paths due to reflections within the sample (see Figure 2).

Figure 2. Schematic of Time Domain OCT System

The photo-detector detects the average intensity over the range of frequencies. The detected signalconsists of a DC term and an interference term that contains the sample information. The use of a dualbalanced approach where a portion of the source signal is subtracted through the use of a secondphoto-detector before digitizing the signal, can be used to remove the DC term at least partially [10].

The sample information is contained in the cross interference that can be written as a function of pathdifference, Δz, between the sample and reference as following the notations in [31].

Here, hair is the refractive index in air, c is the velocity of light, and g(t) is the complex temporal coherencefunction of the laser source, which is related to the source intensity spectrum, S(w) through the Fouriertransform, i.e.,

Similarly, h(t) is the equivalent temporal response of the sample related to the sample frequency responseby:

This response describes the reflections from all the structures within the sample in the z direction and canbe written as:



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where, r(w,z) represent the back-scattering coefficients from the sample structures and h(w,z) is therefractive index. Both these terms are depth and frequency dependent. Physically, the sample temporalresponse is related to sample structure in the z direction through the relation between the time of flightand the distance traveled by the light source.

A low-coherence source is characterized by small width of the temporal coherence function, g(t). Theequation above shows that the detected interference signal only consists of sample information in theneighborhood of Δz as determined by the corresponding time of flight difference. The axial resolution isthen related to the width of the temporal coherence function of the source. For a single reflecting surfaceat the sample with path difference of Δz between the sample and reference, h(t) is a Dirac delta function

at leading to the received interference signal as:

Clearly for single reflecting sample, the detected interference is a cosine modulated signal modulated withthe shape of the envelope of the temporal coherence function.

As the path difference Δz is changed by moving the reference mirror, the received signal picks upinformation about the sample structure with varying depth (within the limit of light remaining collimated inthe sample). This allows scanning of the sample in the axial or depth direction. Such a scan is oftenreferred to as an A-scan. Figure 3 shows an example of received intensities with a sample having tworeflecting surfaces. Two and three dimensional OCT images can be constructed by stacking severalA-scans that are obtained by orthogonal displacements of the beam/sample using an x-y galvanometer.

Figure 3. Example of Received Signals With Two Reflecting Surface



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2.2 Spectral Domain Systems (SD-OCT)

Figure 4 represents a schematic diagram of the SD-OCT system. A broadband-source of light with shorttemporal coherence length is again used as an input to the interferometer. The depth information isobtained by measuring the spectral density in the detection arm of the interferometer using aspectrometer, where the interference beam is dispersed by a diffraction grating and the individualwavelength components are detected by an array detector. In SD-OCT systems the path difference Δzremains fixed and can be assumed to be zero without loss of generality. The received spectrum can thenbe written as [31].

The first term represents a DC value. It is common to perform background subtraction by shutting off thesample arm that allows collection of the DC term and then subtracting this from the measured value withthe sample present.

The following equation shows what is left once the DC term is subtracted:

The depth resolved sample structure is then obtained through the Fourier transform of the above, i.e.:

Figure 4. Schematic of Spectral Domain OCT System

The CCD samples the spectrum from wmin and wmax with w0 being the center frequency assuming that theminimum and maximum frequency is chosen so that aliasing is not an issue. The fast Fourier transform isthen used on this discrete data. Hence, effectively, the sampled spectrum can be considered as ademodulated version of I'(w}. This shows that the axial resolution, in the case of SD-OCT, continues to bedetermined by the width of the temporal coherence function, g(t), of the source, demodulated to DC.

Due to the capture of only the real part of the interference and due to symmetry in the FFT, only half of thesamples at the output of the FFT carry independent information. Techniques known as phase shifting canbe used to capture the phase information as well [18]. This technique captures the interference withvarying phase of the light and then reconstructs the complex interference. This technique is able to doublethe axial depth of measurement compared to conventional SD-OCT systems.



Received Interference Signal

Array Detector

Wavelength


In practice, the array detector serves to digitize the received spectrum in frequency. However, there are acouple of important things to note about this digitization:

• The diffraction grating and array detector combination results in sampling the spectrum linearly inwavelength. The FFT operation normally used to perform the Fourier transform requires spectrumsamples to be linear in frequency or k-space. Therefore, a re-sampling is usually needed before takingthe FFT.

• The array detector has finite width, which means it integrates the spectrum over a finite wavelength.Therefore, the sampling cannot be described by usual Dirac delta function but with a box function withwidth equal to the pixel width. This finite width causes loss of sensitivity with the depth measurement[39].

Figure 5 shows an example of the interference signal with Gaussian source with a single reflecting surfacefor sample for SD-OCT system.

Figure 5. Example of Received Interference Signal Captured on an Array Detector

The main advantage of the SD-OCT system is that the entire depth profile (A-Scan) is measured from asingle spectrum with no mechanical scanning of the reference path. This permits faster acquisition ofA-scans using a line scan CCD array. The use of a fast spectrometer has made video-rate imagingpossible with this technique. High-speed acquisition without any moving parts minimizes any distortion inthe OCT images due to motion in the sample. SD-OCT systems offer a fundamental sensitivity advantageover TD-OCT systems [6], [7], [19]. Further, in shot noise limit, the theoretical signal-to-noise (SNR) ratioof the SD-OCT system is independent of the spectral bandwidth of the light source. Therefore, the axialresolution of the system, which is dependent on the bandwidth of the source, could be increased withoutany deterioration of the SNR.

2.3 Swept Source Systems (SS-OCT)

An alternative way to obtain the spectrogram is to use a frequency-swept laser or a tunable laser with justa single detector, which is referred to as SS-OCT [15]. In SS-OCT like in SD-OCT, no moving parts arerequired for axial scan (ignoring tuning mechanism of the laser source). Figure 6 represents a schematicof a SS-OCT system. These systems require rapid tunable, narrow line-width lasers, which usehigh-speed analog-to-digital (A/D) converters and single-point detectors rather than bulky spectrometers.

Instead of sampling the received spectrum over a finite wavelength, the sample is simply probed withnarrow band but frequency varying source. Another equivalent interpretation is that the sample is probedwith chirp like signal source and the receive signal is a beating of reflections from the reference and fromthe samples. In any case, once the data is captured the operations are the same as in SD-OCT. InSS-OCT, however, a dual-balanced detection is also feasible as in TD-OCT to remove the DC beforedigitization. Therefore, in SS-OCT, the full dynamic range can be used to capture the interference signal.



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Figure 6. Schematic of Swept Source OCT System

2.4 Resolution

2.4.1 Axial Resolution

Axial resolution is an important parameter in OCT systems. It is used to measure how fine the structurescan be resolved in the depth direction. In all types of OCT systems, the achievable axial resolution dependon the temporal coherence length of the light source. Axial resolution can be improved by the use ofbroadband source of light.

The bandwidth of the source spectrum is usually defined by the full width half maximum (FWHM) of thesource intensity spectrum. This is the difference between the two points in the spectrum, which is at halfthe peak value of the spectrum. The corresponding measure in temporal coherence function is known asthe coherence length, lc, of the source. The axial resolution of OCT systems is generally taken to be thesame as this coherence length.

For Gaussian sources, it is possible to derive a closed form expression for the coherence length given by[28],

Here, h is the material refractive index. However, for this equation to hold good, the dispersion in thereference sample arm must be matched. The axial resolution of the system varies on the nature of thebroadband source. In general, the source is never strictly Gaussian. Further, chromatic dispersiondegrades the resolution of OCT since dispersion tends to increase the signal width. The effect ofdispersion can be reduced by choosing a light source with an optimum central wavelength at which thegroup velocity dispersion is negligible and by the use of appropriate dispersion compensation schemes.



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www.ti.com Basic Signal Processing Chain in OCT Systems

2.4.2 Lateral Resolution

Lateral resolution is determined by the numerical aperture of the sampling lens using Abbe’s law [9], [31].

where NA is the numerical aperture of the microscope objective. Though, a higher numerical apertureenhances the lateral resolution, the depth of focus, Z, is narrowed as indicated in the following equation[9], [31].

where, h is the sample refractive index. A typical Z for a small NA system is several hundred microns,which is about 10 orders smaller than the scanning depth range of an OCT system. Limited Z of high NAobjectives restricts the axial scanning range. Dynamic focusing or en face images that are obtained byfocusing high NA objective further into the sample providing a series of two-dimensional depth scans cancompensate for this problem to a certain extent [31].

Several numerical techniques to improve the lateral resolution have been reported in literature [23], [38].

3 Basic Signal Processing Chain in OCT Systems

Though the first generation of OCT systems was based on time domain systems, the popularity offrequency domain systems (whether spectral or swept source) are increasing due to their speed ofacquisition and due to improved sensitivity. This section concentrates on the signal processing chain forfrequency domain systems only.

3.1 Background Subtraction

To eliminate the reference power term, the reference spectrum from only the reference arm is detectedand subtracted from the interference spectrum. The reference spectrum is acquired at the beginning ofevery image acquisition to account for fluctuations in the source between measurements. It may also befeasible to derive the reference spectrum from the acquired data since the interference is usually highfrequency fringes, whereas, the background term has low frequency components.

In swept source systems, using dual-balanced photo-detectors allows this subtraction in analog domain.

3.2 Re-Sampling

The interference produces fringes, which are detected by a spectrometer using a CCD or photodiodearray detector. In SD-OCT systems, spectrometers measure optical intensity as a function of wavelength.Dispersion results from the non-linear function of the phase dependency of wavelength l. In order to applythe fast Fourier transform (FFT) reconstructing the axial scan as a function of depth, the spectrum shouldbe evenly sampled in k-space. Therefore, the spectrometer output must be transformed from thewavelength to the frequency space. Following the method used in [14], N linearly spaced k values are

defined between the range covered by and (the maximum and minimum wavelength recorded).

Each of the corresponding to the linearly spaced kI can be related through a non-linearity parameter SI

as follows:



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MagnitudeComputation

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Basic Signal Processing Chain in OCT Systems www.ti.com

Using the equations above, non-linearity SI can be written as a function of I.

The equation above defines an array of real numbers , which defines the new interpolationsampling points to resample the recorded discrete spectrum in order to obtain linearly sampled spectrumin k space.

A couple of generic techniques for re-sampling are as follows:

• Linear interpolation: The spectrum is linearly interpolated between two recorded consecutive samples.This is simple and efficient but numerically less accurate resulting in errors at greater depths.

• Cubic B-spline interpolation: This is computationally more expensive but is more accurate.

The accuracy of any interpolation like linear or spline as mentioned above can be improved by firstup-sampling the data. It is usually performed by using an FFT, zero padding and then performing IFFT.Usually two to four times up-sampling is sufficient for this application.

The above analysis assumes that the data is recorded linearly in wavelength domain. However, due toconstruction effects, the grating/array detector combination may not result in exact linearly spacedwavelength recording of the received spectrum. It is common to use a third order polynomial to capturethe non-linear mapping between the k-space and wavelength. The non-linearity can then be expressed as:

The coefficients b1 and b2 can be computed either through a calibration mechanism or through auto focusalgorithms.

Some systems for swept source-based OCT uses a non-linear clocking scheme where the clocks arederived from a second interferometer so that the data acquisition becomes linear in k-space. Such asystem can avoid the re-sampling step [29].

3.3 Image Formation (FFT)

The basic operation to get the depth resolved A-scan from the interference fringes is the FFT. Thestructural image is obtained by taking the magnitude of the complex FFT output; each FFT creates aparticular A-scan. By moving the galvanometer in x direction, the successive A-scan line is created, whichis stacked together to create a B mode image. By moving the galvanometer in both x-y direction, a full 3Dvolume can be generated.

Figure 7 and Figure 8 illustrate the steps needed to create the depth resolved information of a singleA-scan from the interferogram.

Figure 7. Image Formation Path

Figure 8. Representation of Signals in the Signal Chain



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www.ti.com Basic Signal Processing Chain in OCT Systems

3.4 Display

Two dimensional OCT images are typically represented using a density plot. The horizontal axis typicallycorresponds to the direction of transverse scanning and the vertical axis corresponds to the scanningdepth. A gray level is plotted at a particular pixel on an image corresponding to the magnitude of the depthprofile at a particular depth and transverse scanning position.

Due to the high dynamic range, pixel intensity range is compressed before displaying it. It is common touse the logarithmic non-linearity to perform such compression. Alternately, a look-up tables-basedcompression can be used. Sometimes, color look-up tables are used instead of simple gray levels for thefinal display to bring out clinically relevant information better in the displayed image. It is also necessary tomatch the actual data collected to the display size. Bilinear interpolation is employed for this type ofconversion of data collection co-ordinate system to the display co-ordinate system, which is commonlyknown as scan conversion.

As 2D images may be insufficient to recognize features of interest, e.g., a blood vessel or a tissueboundary, 3D volume is created by collecting the A-scan line over x-y direction. This requires very fastdata acquisition and processing systems. In such case, various 3D rendering techniques like ray tracing ormaximum intensity projection (MIP) is used to display the data.

3.5 Image Enhancement

Speckle noise that arises from the interference between coherent waves backscattered from nearbyscatters in a sample is the dominating source of noise in OCT images. Usually, non-linear directionpreserving digital filters are used to improve the image quality [25]. Simple examples of such filters includemean and median filters. More advanced directional filters such as wavelet, anisotropic or bi-lateral filtersare also used in reducing the noise while preserving the edges.

Simple signal averaging over the same line can also be used to improve the signal-to-noise ratio of thedata collected at the cost of reduced frame rate [26].

Involuntary movements of the sample during image scans can limit the performance of the OCT systems.A secondary camera is sometimes used to track such involuntary movements and control the dataacquisition in a closed loop manner [11].

3.6 Dispersion Compensation

The refractive index of the biological tissues is, in general, frequency dependent slowing down certainoptical frequencies to a greater extent than others, therefore, dispersing the light. Dispersion correctioncan take place both in the hardware and the software.

• A considerable amount of dispersion can be corrected, if the dispersions in both the reference andsample arms of the interferometer are equal and matched properly.

• One can balance dispersion in an OCT system by inserting variable-thickness, BK7, and fused silicaprisms in the reference arm.

These hardware-based methods can compensate material induced dispersion but the sample beingimaged itself could also be dispersive. In that case, an automated numerical method of dispersioncompensation is desirable.

In spectral OCT, dispersion compensation can be performed by cancelling the frequency dependentnonlinear phase, which arises from the dispersion mismatch between the two arms of the interferometer.Dispersion compensation can be applied to this signal via a phase correction. The applied phasecorrection is computed as:

where a2 is adjusted to compensate for the group velocity dispersion imbalance and a3 is adjusted tocompensate for the third-order dispersion imbalance. Usually, dispersion up to the third order is sufficientassuming that the interferometer arms were approximately dispersion matched initially.



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Advanced Signal Processing in OCT Systems www.ti.com

3.6.1 Auto-Focusing

Auto-focus algorithms are designed to automatically estimate the coefficients, a2, and a3. Severaltechniques have been proposed in literature.

Figure 9 shows a schematic representation of the process Wojtkowski et al. [32]. The dispersioncompensation is performed after background subtraction and re-sampling. The real-fringe data isconverted to its analytic equivalent by the Hilbert transform. Phase correction is applied to this complexdata before taking the FFT to generate the structural information of the sample. The metric used foroptimizing the coefficients, a2, and, a3, is defined to be one divided by the total number of points in theaxial scan intensity, which are above a predetermined threshold. The actual optimization is done via bruteforce search of over the parameter space.

Figure 9. Dispersion Compensation per Wojtkowski et al. [32]

In [21], Marks et al. have used a metric that is the power sum of the magnitude of the calculated samplereflectance function around a dominant reflection point. They have jointly optimized the re-sampling aswell as phase non-linearity. The overall scheme is shown in Figure 10. They perform an intelligent searchover the parameter space using the bracketing and Golden section technique. The proposed signal chainincludes Wiener filtering for optimum noise performance, followed by phase rotation for dispersioncompensation and re-sampling and finally FFT.

Figure 10. Dispersion Compensation per Marks et al. [21]

4 Advanced Signal Processing in OCT Systems

This section provides a brief overview of some of the advancements and new imaging modes based onoptical coherence tomography techniques. These include Doppler imaging, elastography, polarizationsensitive, and spectroscopic OCT imaging. Of these, elastography and Doppler imaging have theircounterpart in ultrasound medical imaging. Polarization related and spectroscopic imaging are unique tothe specific nature of light used in OCT systems.

4.1 Doppler Imaging With OCT

Doppler frequency estimation is used to evaluate the blood flow through various tissues, e.g., in and out ofthe heart, through retinal veins, etc., in modalities such as ultrasound. It is also feasible to estimate theDoppler frequency shift for OCT systems [24], [36]. Once the Doppler frequency shift has been identified,the velocity of the fluid can be estimated using the following equation:



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www.ti.com Advanced Signal Processing in OCT Systems

where fd is the Doppler frequency, is the center wavelength of the source and q is the angle betweenthe light propagation direction and the blood flow direction.

Doppler imaging can be carried in any type of OCT systems: time domain, spectral radar or swept source.In the spectral domain, after typical processing including re-sampling, dispersion compensation, noisefiltering, and FFT, the amplitude and phase of the axial scan is given as a function of distance. Thedifference of phases of successive axial scan lines along the same direction in the sample can be used tomeasure the Doppler frequency. An alternate technique to estimate the Doppler frequency is the Kasaialgorithm that has been used successfully in ultrasound applications [16], [36].

4.1.1 Doppler Frequency Estimation Using Kasai Algorithm

The Kasai algorithm uses multiple axial scan lines along the same direction of the sample. This set ofmultiple scan lines is known as ensemble in ultrasound literature. Assume that the number of axial scanlines in an ensemble is N. Also assume that a window of length M is used in the axial direction in theestimation. The Kasai algorithm starts by estimating the auto-correlation at unity lag (in discrete domain).Therefore, assuming that the complex axial scan line values are Am,n (the value of the output of FFT forthe mth depth point and nth scan line in an ensemble), the auto-correlation at unity lag is given by

Then the Doppler estimate is given by

Here, fa represents the axial scan line repetition rate.

It is also possible to estimate the turbulence, which is a measure of the quality of blood flow. This requiresthe additional calculation of the auto-correlation at zero lag,

The turbulence can then be computed as

Based on the above computations, the signal chain of Doppler imaging with OCT systems are shown inFigure 11.

Figure 11. Doppler Imaging Signal Chain Using Kasai Algorithm for OCT Systems



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4.2 Elasticity Imaging With OCT

Elasticity imaging is imaging of the elastic behavior of biological samples. Due to very high resolution inOCT systems, elastographic techniques allow the study of microscopic deformation of biological tissues[27]. The main measure of tissue stiffness is the elastic modulus that is known to vary widely for differenttissue types. A number of tissue diseases alter the elastic modulus; therefore, imaging the elastic modulusprovides crucial clues to tissue diseases including assessment of malignancy.

Elasticity imaging is carried out under compression. Techniques include imaging under two or morecompression setting and pulsating compressions. One typical technique is to measure the displacement oftissue under two different compressions. The technique commonly used for measuring suchdisplacements is called speckle tracking [3], [27]. This technique can be used with any OCT systemsincluding time domain, spectral radar or swept source systems. After determining the axial scan linevalues (through noise filtering, re-sampling, dispersion compensation, and FFT for frequency domainsystems), a two dimensional local cross-correlation in a pre-defined window of size M1 × M2 is computed.This cross-correlation is given by:

Here, Xi,j represent the pixel values at one compression and Yi,j the pixel values at the secondcompression with X and Y being the corresponding average value over the chosen window. Note that thecross-correlation is close to one in the correlated region and to zero in uncorrelated regions. Therefore, bysearching for the maximum of the cross-correlation over the chosen window, the local displacement canbe estimated. The lateral and axial displacement can then be presented into separate images or becombined to form a single image for view.

The above technique is a case of displacement imaging. In ideal elasticity imaging, the ultimate goal is toderive the elastic modulus. Quantitative derivation of elastic modulus requires solving the inverse problem.This is an active area of research in both ultrasound and OCT imaging modalities. In OCT, someadvanced techniques that use optimization methods using variational framework with a priori knowledgeabout biological tissue deformation have been reported in literature [5], [17].

The medical value of elasticity imaging in OCT is still under investigation [3].

4.3 Polarization Sensitive OCT

4.3.1 Polarization Sensitivities of Biological Tissues

Biochemical composition has a tendency to change polarization state as light goes through or arereflected back from them due to their highly organized molecules. Therefore, the polarization state of therecorded light in OCT provides information regarding the bio-chemical structure of the tissues and can beused to reveal the bio-chemical composition of the tissue. Therefore, polarization sensitive OCT allowsmore of molecular or spectroscopic imaging rather than pure structural imaging that is performed innormal OCT systems.

Three separate mechanism of altering the polarization state through biological tissues are of importance toOCT imaging [3]:

• Birefringence: Here the light propagation velocities (refractive index) are dependent on the spatialorientation of a biological sample, thus, the change in polarization states varies with the direction ofincident light.

• Dichroism: This refers to the case where one polarization state is filtered but its orthogonal statespasses through.

• Optical rotation: This rotates the axis of polarization states.

The use of these features in polarization state changes in biological tissues is an active area of researchin medical imaging community.



PolarizedBeamSplitter

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Half-WavePlate

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DiffractionGrating


4.3.2 Polarization Sensitive OCT

Polarization sensitive OCT systems can be designed to be of both time domain and frequency domaintypes. Due to higher speed of acquisition and higher sensitivities, frequency domain polarization sensitiveOCT systems are getting popular. Several such implementations reported in literature are described in thissection.

The common features of all polarization sensitive OCT is the addition of a polarizer to provide a knownpolarization state of the source as shown in Figure 12. Additional elements are also included in the opticspath to optimize the system. These include:

• Quarter wave plate (QWP) or half wave plates (HWP): These provide proper rotations of thepolarization states to match the optical elements preceding and following them.

• Polarization controllers (PC): These are used to fine tune the polarization states.• Polarization modulators (PM): These elements are used to switch the polarization states of the source.• Polarizing beam splitter (PBS): These devices split the beam into its orthogonal polarization states.

Figure 12. Example of a Polarization Sensitive OCT System Using Two Line Scan Camera

There are differences in the way the receiver is designed for PS-OCT systems in spectral domain. Here isan example of some variations of receiver designs:

• One single line camera design for spectral radar systems: In this design, the spectrometer is designedin such a way that the orthogonal polarizations states of receive light is focused on different pixels of asingle line CCD camera. In the design by Cense et al. [4], a 2048 single line CCD camera is used. Thefirst 1024 pixels were used to capture one polarization state and the next 1024 pixels are used tocapture the orthogonal polarization state.

• 2D single camera design for spectral radar systems: In this design, a 2D camera is used where the twodifferent polarization states are focused on different lines of the CCD camera [37]

• Two single line camera design for spectral radar systems: In this design the polarization states areseparated by polarizing beam splitters and then focused on two separate single line CCD cameras[12], [35].

• Two detector design for swept source systems: In this design a swept source laser is used. Thereceiver is then simply two sets of detectors whose inputs are the two orthogonal polarizations statesseparated using a polarizing beam splitter [40].



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The basic operations for the spectra of the orthogonal polarization states of the received light capturedthrough either line scan CCD camera (for broadband source) or through detectors (for swept source) arethe same as normal spectral domain processing. These include re-sampling, dispersion compensation,noise filtering, and FFT. Once FFT is performed, the amplitudes and phases of the two orthogonal states(vertical and horizontal) as a function of depth are obtained. Note that the received complex vectors for thetwo polarization states as a function of depth, Z , by:

Then the polarization independent reflectivity, R, the retardation, d, and the optics axis orientation, q, canbe defined as [12]:

The retardation, d, is a measure of birefringence of the optical tissue and the optics axis orientation, q, is ameasure of optical axis rotation in the tissue. By imaging these three parameters above, the structural, thebirefringence and the optical axis rotation of the biological samples are actually being imaged. Figure 13shows the signal processing chain for these types of polarization sensitive OCT imaging.

Figure 13. Signal Processing Chain in Polarization Sensitive Spectral Domain OCT

Light polarization is sometimes described via the 4-tuple known as Stokes Vectors and correspondingMuller and Jones matrix. The PS-OCT measurements can also be used to determine the Stokes Vectorsas follows [12].

It is possible to provide the images of individual components of Stokes vectors (four images) [13].



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Techniques have also been explored to obtain the Jones and Mueller matrix of the biological sample. Thistechnique involves the use of polarization modulator, [37]. This way the source light can be polarized intotwo orthogonal polarized states; for each of the source polarization states, two receive polarization can bedetermined. Therefore, you have the input and output vector for the Jones calculus from which the fullJones matrix can be determined, which can then be used to determine the Mueller matrix. In this case, theviewing represents the individual components of the Mueller matrix (total of 16 images) or the phase andamplitude of individual components of the Jones matrix (total of eight images).

4.4 Spectroscopic OCT

Spectroscopic OCT (SOCT) analyzes the frequency dependencies of the absorption of signal in OCTsystems. SOCT has been demonstrated in the context of both time domain systems [1], [22], [33] andfrequency domain systems [20], [34].

In time domain SOCT systems, the system is very typical of TD-OCT systems. The time depth resolveddata from the photo detector is sampled at very high rate. Several techniques have been proposed foranalyzing the data wavelength dependencies. A short time Fourier transform (STFT) can be used in thedepth direction to determine localized absorption as a function wavelength [1], [33]. For better wavelengthselectivity, a chirped Z transform (CZT) is proposed in [1]. A wavelet transform (e.g., Morlet wavelet)providing varying wavelength-localization property has also been studied [22].

In spectral or frequency domain SOCT systems, the front end processing is similar to typical SD-OCTsystems, i.e., it includes background subtraction, re-sampling of the fringe data into linear spaced data in kspace domain. At this point an FFT can be taken to obtain the depth resolved reflectivity information. Thiscan be followed by localized Fourier analysis with any of techniques used in time domain SOCT systems[34]. Figure 14 shows the processing steps of such a system.

Figure 14. Spectroscopic Data Generation in Frequency Domain OCT

An alternate approach is to multiply the recorded fringe data (after re-sampling) by a frequency windowcentered at the wavelength of interest and then take the Fourier transform [20]. Specifically, this techniquedetermines the following equation:

Where W(w-w0,Δw) represents a window around the frequency of interest, w0 with a bandwidth of Δw andI'(w) is the recorded spectrum. The choice of the window bandwidth determines the resolution depth andwavelength for this spectroscopic analysis. The processing steps for this method are shown in Figure 15.

Figure 15. Spectroscopic Data Generation in Frequency Domain OCT With Frequency DomainWindowing



DSP for OCT Signal Processing www.ti.com

5 DSP for OCT Signal Processing

For details of benchmarking of the key signal processing algorithms needed to produce a B-mode image,see [2]. This benchmarking was done on Texas Instruments’ C64x+™ DSP architecture. TI’s DSP portfolioincludes several devices based on TMS320C64x+™ DSP. These devices vary in the number of C64x+cores available, the speed of the core, the amount of memory, interfaces, etc. This benchmarking showsthat TI’s multi-core device, like the TMS320C6472, is capable of handling processing of scan-lines at arate from 35 K lines per second to 100 K lines per second depending on the configuration. The processingrate variation is due to the amount of signal processing that is needed to be done, i.e., the addition ofadditional processing for dispersion compensation reduces the processing rate. These numbers show thatsuch devices are quite capable performing the OCT signal processing needs. These devices also comewith very high bandwidth data input/output capabilities. The TMS320C6472 device has two serial rapid I/O(SRIO) interface with the total capability of 5 Gbps bi-directional throughput.

The DSP-based OCT systems have been reported in literature with the use of multiple DSPs [30]. Theadvent of multi-core DSPs with advanced features allows the use of single such device in OCT systems.

DSPs provide several advantages for the implementation of OCT systems such as:

• TI has several variations of processors based on C64x+ architecture. The OCT system manufacturerhas the ability to choose one of these devices to suit their need based on processing capability, I/Orequirement, memory available, cost and power. Since these devices are based on the same core, themanufacturer can quickly move to a different device without major software change to address newmarket needs.

• These devices allow development of OCT systems at a fractional power compared to x86 or graphicsprocessing unit (GPU) based units while maintaining the same programmability feature that is essentialfor field upgrades as well as for new applications.

• Within limits of processing capabilities, the same device can be used to perform various modes ofoperations like B-mode imaging, Doppler, polarization sensitive, etc. These modes of operations differin post-processing after the post FFT complex image is formed.

• Due to programmability, the same processing unit used for main signal chain can be utilized forcalibration and different estimation algorithms needed to identify system parameters (like backgroundsignal, re-sampling points, phase corrections for dispersion compensation, etc.). These parameters areeither pre-computed during calibration or computed automatically before the image acquisition process.In an FPGA-based systems, separate data paths would be needed to perform these functions.

• Due to smaller footprint, DSP-based systems allow the development of smaller, low power, low cost aswell as battery-operated portable systems.

Based on the understanding and analysis of OCT systems as well as the capabilities of current and nextgeneration DSPs, DSP will play a very similar role to OCT that it has played in other imaging modalities,like ultrasound, to develop low-power cost effective solution. Therefore, DSPs allow more ubiquitous useof OCT systems in medical imaging and diagnostics.

6 Conclusion

OCT is a new imaging modality somewhat comparable to ultrasound in that it provides structuralinformation without ionizing radiation. Since it uses frequency ranges in visible or near infra red spectrum,the resulting resolution is in the order of µm. The depth of penetration is low compared to ultrasound (inthe range of few mm). Like ultrasound, Doppler and elasticity imaging is also possible. In addition,polarization sensitive and spectroscopic imaging modes allow additional information regarding thebiological tissues to be imaged.

OCT has been used both ex vivo and in vivo. It has also been used non-invasively as well as in minimallyinvasive in vivo imaging. Imaging via endoscopic and needle like instruments allow localized imaging offine structures in tissues. Intra-operative use of OCT systems to allow better visualization during surgeryhas also been reported.



www.ti.com References

The signal processing of the more popular spectral domain or swept source OCT system is dominated byFFT operations. Several application dependent pre and post processing is needed to perform noisereduction, dispersion compensation, image enhancement as well as estimation of additional parameterslike flow velocity, elasticity, polarization parameters, etc. All of these processing are well suited forembedded implementation on TI DSPs. TI multi-core DSP family along with SoC-based on C64x+architecture provides a scalable and programmable low power, low cost platform for implementing OCTsystems for various applications.

7 References1. D. C. Adler, T. H. Ko, P. R. Herz, and J. G. Fujimoto, Optical Coherence Tomography Contrast

Enhancement Using Spectroscopic Analysis with Spectral Auto-Correlation, Optics Express, pp.5487-5501, Vol. 12, No. 22, Oct. 2004.

2. Algorithms for Optical Coherence Tomography on TMS320C64x+ TI DSP (SPRABB7)3. M. Brezinsky, Optical Coherence Tomography, Elsevier, 2006.4. B. Cense, M. Mujat, T. C. Chen, B. H. Park, and J. F. de Boer, Polarization-Sensitive Spectral-Domain

Optical Coherence Tomography Using a Single Line Scan Camera, Optics Express, pp. 2421-2431,Vol. 15, No. 5, Mar. 2007.

5. R. C. Chan, A. H. Chau, W. C. Karl, S. Nadkarni, A. S. Khalil, N. Iftimia, M. Shishkov, G. J. Tearney,M. R. Kaazempur-Mofrad, and B. E. Bouma, OCT-Based Arterial Elastograohy: Robust EstimationExploiting Tissue Biomechanics, Optics Express, pp. 4558-4572, Vol. 12, No. 19, Sep. 2004.

6. M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, Sensitivity Advantage of Swept Source andFourier Domain Optical Coherence Tomography, Optics Express, pp. 2183-2189, Vol. 11, No. 18,Sept. 2003.

7. J. F. de Boer, B. Cense, H. P. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, ImprovedSignal-to-Noise Ratio in Spectral-Domain Compared with Time-Domain Optical CoherenceTomography, Optics Letters, pp. 2067-2069, Vol. 28, No. 21, Nov. 2003.

8. W. Drexler, and J. G. Fujimoto (ed.), Optical Coherence Tomography: Technology and Applications,Springer, 2008.

9. Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, High-Resolution Optical Coherence TomographyOver a Large Depth Range with an Axicon Lens, Optics Letters, pp. 243-245, Vol. 27, No. 4, Feb 2002.

10. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Optical Coherence Tomography-Principles and Applictions, Reports on Progress in Physiscs, pp. 239-303, Vol. 66, Jan. 2003.

11. R. D. Ferguson, D. X. Hammer, L. A.. Paunescu, S. Beaton, J. S. Schuman, Tracking OpticalCoherent Tomography,” Optics Letters, pp. 2139-2141, Vol. 29, No. 18, Sept. 2004.

12. E. Gotzinger, M. Pircher, B. Baumann, C. Ahlers, W. Geitzenauer, U. Schmidt-Erfurth, and C. K.Hitzenberger, Three-Dimensional Polarization Sensitive OCT Imaging and Interactive Display of theHuman Retina, Optics Express, pp. 4151-4165, Vol. 17, No. 5, Mar. 2009.

13. E. Gotzinger, M. Pircher, and C. K. Hitzenberger, High-Speed Spectral Domain Polarization SensitiveOptical Coherence Tomography of the Human Retina, Optics Express, pp. 10217-10229, Vol. 13, No.25, Dec. 2005.

14. B. Grajciar, and O. Ondracek, Dispersion Compensation in Spectral Domain Optical CoherentTomography, available at http://www.urel.feec.vutbr.cz/ra2008/archive/ra2006/abstracts/056.pdf.

15. R. Huber, D. C. Adler, V. J. Srinivasan, and J. G. Fujimoto, Fourier Domain Mode Locking at 1050 nmfor Ultrahigh-Speed Optical Coherence Tomography of the Human Retina at 236,000 Axial Scans perSecond, Optics Letters, pp. 2049-2051, Vol. 32, No. 14, 2007.

16. C. Kasai, K. Namekawa, A. Koyano, and R. Omoto, Real-Time Two Dimensional Blood Flow ImagingUsing an Autocorrelation Technique, IEEE Trans. on Sonics and Ultrasonics, pp. 458- 464, vol. SU-32,No. 3, May 1985.

17. A. S. Khalil, R. C. Chan, A. H. Chau, B. E. Bouma, and M. R. Kaazempur-Mofrad, Tissue ElasticityEstimation with Optical Coherence Elastography : Toward Mechanical Characterization of In Vivo SoftTissue, Annals of Biomedical Engineering, pp. 1-9, Vol. 33, No. 11, Nov. 2005.

18. R. A. Leitgeb, C. K. Hitzenberger, T. Bajraszewski, and A. F. Fercher, Phase Shifting Algorithm toAchieve High-Speed Long Depth Range Probing by Fourier Domain Optical Coherence Tomography,”Optics Letters, pp. 2201-2203, Vol. 28, No. 22, 2003.



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http://www.urel.feec.vutbr.cz/ra2008/archive/ra2006/abstracts/056.pdf

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20. R. A. Leitgeb, M. Wojtkowski, A. Kowalczyk, C. K. Hitzenberger, M. Sticker, and A. F. Fercher,Spectral Measurement of Absorption by Spectroscopic Frequency-Domain Optical CoherenceTomography, Optics Letters, pp. 820-822, Vol. 25, No. 11, Jun. 01, 2000.

21. D. L. Marks, A. L. Oldenburg, J. J. Reynolds and S. A. Boppart, Autofocus Algorithm for DispersionCorrection in Optical Coherence Tomography, Applied Optics, pp. 3038-3046, Vol. 42, No. 16, Jun.2003.

22. U. Morgner, W. Drexler, F. X. Kartner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto,Spectroscopic Optical Coherence Tomography, Optics Letters, pp. 111-113, Vol. 25, No. 2, Jan. 2000.

23. T S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, Real-Time Interferometric SyntheticAperture Microscopy, Optics Express, pp. 2555-2569, Vol. 16, No. 4, Feb. 2008.

24. A. M. Rollins, S. Yazdanfar, J. K. Barton, and J. A. Izatt, Real-Time in Vivo Color Doppler OpticalCoherence Tomography, Journal of Biomedical Optics, pp. 123-129, Vol. 7, No. 1, Jan. 2002.

25. J. Rowgowska, and M. E. Brezinski, Image Processing Techniques for Noise Removal, Enhancementand Segmentation of Cartilage OCT Images, Physics in Medicine and Biology, Vol. 47, pp. 641-655,2002.

26. B. Sander, M. Larsen, L. Thrane, J L Hougaard, and T.M. Jorgensen, Enhanced Optical CoherenceTomography Imaging by Multiple Scan Averaging, British Journal of Ophthalmology, pp. 207-212, Vol.89, 2005.

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28. J. M. Schmitt, Optical Coherence Tomography (OCT): A Review, IEEE J. of Selected Topics inQuantum Electronics, pp. 1205-1215, Vol. 5, No. 4, Jul/Aug. 1999.

29. V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G.Fujimoto, Ultrahigh-Speed Optical Coherence Tomography for Three-Dimensional and En FaceImaging of the Retina and Optic Nerve Head, Investigative Ophthalmology and Visual Science, pp.5103-5110, Vol. 49, No. 11, Nov. 2008.

30. J. Su et al., Real-Time Swept Source Optical Coherence Tomography Imaging of the Human AirwayUsing a Microelectromechanical System Endoscope and Digital Signal Processor, J. Biomed. Opt., Vol.13(3), 2008.

31. P.H. Tomlins and R.K. Wang, Theory, Developments and Applications of Optical CoherenceTomography, Journal of Physics D: Applied Physics, pp. 2519 - 2535, Vol. 38, Jul. 2005.

32. M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker,“Ultrahigh-Resolution, High-Speed, Fourier Domain Optical Coherence Tomography and Methods forDispersion Compensation,” Optics Express, pp. 2404-2422, Vol. 12, No. 11, May 2004.

33. C. Xu, D. L. Marks, M. N. Do, and S. A. Boppart, Separation of Absorption and Scattering Profiles inSpectroscopic Optical Coherence Tomography Using Least-Squares Algorithm, Optics Express, pp.4790-4802, Vol. 12, No. 20, Oct. 2004.

34. C. Xu, C. Vinegoni, T. S. Ralston, W. Luo, W. Tan, and S. A. Boppart, Spectroscopic Spectral-DomainOptical Coherence Microscopy, Optics Letters, pp. 1079-1081, Vol. 31, No. 8, Apr. 2006.

35. M. Yamanari, S. Makita, V. D. Madjarova, T. Yatagai, and Y. Yasuno, Fiber-BasedPoloarization-Sensitive Fourier Domain Optical Coherence Tomography Using B-Scan-OrientedPolarization Modulation Method,” Optics Express, pp. 6502-6515, Vol. 14, No. 14, July, 2006.

36. V. X. D. Yang, M. L. Gordon, B. Qi, J. Pekar, S. Lo, E. Seng-Yue, A. Mok, B. C. Wilson, and I. A.Vitkin, High-Speed, Wide Velocity Dynamic Range Doppler Optical Coherence Tomography (part I):System Design, Signal processing, and Performance,” Optics Express, pp. 794-809, Vol. 11, No. 7,April. 2003.

37. Y. Yasuno, S. Makita, T. Endo, M. Itoh, T. Yatagai, M. Takahashi, C. Katada, and M. Mutoh,Polarization-Sensitive Complex Fourier Domain Optical Coherence Tomography for Jones matrixImaging of Biological Samples, Applied Physics letters, pp. 3023-3025, Vol. 85, No. 15, Oct. 2004.

38. L. Yu, B. Rao, J. Zhang, J. Su, Q. Wang, S. Guo, and Z. Chen, Improved Lateral Resolution in OpticalCoherence Tomography by Digital Focusing Using Two Dimensional Numerical Diffraction Method.Optics Express, pp. 7634-7641, Vol. 15, No. 12, June 2007.



www.ti.com Acknowledgement

39. S. H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, High-Speed Spectral-DomainOptical Coherence Tomography at 1.3 µm Wavelength,” Optics Express, pp. 3598-3604, Vol. 11, No.26, Dec. 2003.

40. J. Zhang, W. Jung, J. S. Nelson, and Z. Chen, Full Range Polarization-Sensitive Fourier DomainOptical Coherence Tomography, Optics Express, pp. 6033-6039, Vol. 12, No. 24, Nov. 2004.

8 Acknowledgement

The authors would like to express their thanks to Professor Stephen A. Boppart of the University of Illinoisat Urbana-Champaign and Professor James G. Fujimoto of the Massachusetts Institute of Technology.They graciously shared their expertise in optical coherence tomography with us and helped us understandOCT system processing requirements. Professor Boppart hosted us at the Biophotonics ImagingLaboratory at Beckman Institute for Advanced Science and Technology at the University of Illinois atUrbana-Champaign. The system and application understanding we received from him and his team havebeen integral in defining our effort in this medical imaging modality.



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Optical Coherence Tomography for Medical Imaging Overview