Conventional spectral domain interferometry (SDI) methods suffer from the need of data linearization. When applied to optical coherence tomography (OCT), conventional SDI methods are limited in their 3D capability, as they cannot deliver direct en-face cuts. Here we introduce a novel SDI method, which eliminates these disadvantages. We denote this method as Master - Slave Interferometry (MSI), because a signal is acquired by a slave interferometer for an optical path difference (OPD) value determined by a master interferometer. The MSI method radically changes the main building block of an SDI sensor and of a spectral domain OCT set-up. The serially provided signal in conventional technology is replaced by multiple signals, a signal for each OPD point in the object investigated. This opens novel avenues in parallel sensing and in parallelization of signal processing in 3D-OCT, with applications in high- resolution medical imaging and microscopy investigation of biosamples. Eliminating the need of linearization leads to lower cost OCT systems and opens potential avenues in increasing the speed of production of en-face OCT images in comparison with conventional SDI.
© 2013 OSA
Spectral domain interferometry (SDI) is a widely applied measurement technique in different disguises, such as Fourier domain white light interferometry [1,2] or wavelength sweeping interferometry [3,4]. SDI is also the method of choice for modern spectral domain (SD) optical coherence tomography (OCT), used in what is called Fourier domain (FD)-OCT, spectrometer based (Sp)-OCT or swept source (SS)-OCT. SDI and spectral domain (SD)-OCT dominate the fields of interferometry based sensing and OCT respectively due to their higher sensitivity and better signal to noise ratio than their time domain (TD) counterparts. By a fast Fourier transformation (FFT) of the optical spectrum at the interferometer output, a reflectivity profile is obtained, where in one go, all scattering points along the axial range are interrogated. In time domain interferometry and OCT, each scattering point and respectively, layer in depth, are interrogated within separate measuring events.
Despite the advantage of sensitivity and collection of all axial data in one spectral scan, there are several disadvantages that limit the SDI method. A disadvantage of all forms of SDI and SD-OCT is the need for presenting the data in equal frequency slots to the FFT processor. This is known as the problem of linearization or calibration of data acquired. The progress of SD-OCT was only made possible by developing sophisticated and costly hardware and software methods to ensure proper linearization, otherwise sensitivity and resolution suffer. The origin of this drawback in SDI and in SD-OCT is the inherent non-evenly production of signal, resulting from the reading of the channelled spectrum. In Sp-SDI, the geometry of dispersion or diffraction determines a nonlinear dependence of distribution of optical frequencies over the linear array of the camera employed by the spectrometer. To compensate for such dependence, a solution using a prism after the diffraction grating was proposed . However, this complicates the optics hardware, requires careful adjustment, introduces losses and the linearity is not fully re-established. In SS-OCT, for a high tuning speed, the Fabry-Perot tunable filter is excited with sinusoidal signals. This determines a nonlinear dependence of the optical frequency of the signal generated versus time. Several reports exist in literature, where the swept source is equipped with a supplementary clock. This is based on a high finesse cavity and a faster photo-detector than that used in the main OCT channel, to provide calibrated frequency values and so, such solution complicates the optics and the electronic hardware [6,7]. This method, based on clock pulses, is one of the most used techniques in conventional SDI and this was also employed here to provide the data for the conventional SS-OCT technique. The clock is incorporated into the swept source, and adds to the cost of the source. Other methods modulate the shape of the signal applied to the tunable filter . Such a procedure however needs to be customized for each tunable filter in the swept source.
For better data sampling before FFT, zero padding is often needed . This requires extra time. Additionally, specific FFT signal processing methods, linearization and calibration procedures have been developed and all these take time and require significant computational resources.
Signal conditioning for linearization of data is a major bottleneck in SDI and therefore, several techniques have been devised to reduce the post-processing time by eliminating the need of data re-sampling [10,11]. All proposed methods, either hardware or software, require additional equipment, complicate the SDI or SD-OCT set-up, require customization of devices or extra dedicated software. All these raise the cost of sensing and of OCT systems. In addition, whatever complex, such methods are imperfect and the linearization achieved is far from perfect.
As another disadvantage of the SDI method, because the FFT delivers data along the axial direction only, production of an en-face image, similar in orientation to an image provided by a microscope, requires resources and time. So far, TD-OCT systems were uniquely positioned to provide in real-time, high-resolution T-scan based en-face images by simply transversally scanning the optical beam over the sample . Unfortunately, TD-OCT is slow and can provide accurate en-face images for nearly static samples only. As another disadvantage, in TD-OCT, a single en-face image is produced at any given time for a single depth. In order to generate an image from a different depth, the optical path length of the reference arm needs to be re-adjusted and the image acquisition repeated.
SD-OCT is renowned for its ability to produce high-speed, high-resolution cross section (B-scan) images of the sample under investigation [13,14]. However, often biomedical applications require that an en-face OCT image is produced alongside B-scan images, for better visualization of microstructures, due to the additional information conveyed that enhances the physician’s understanding of the underlying pathology .
Both implementations of the SD-OCT, Sp-OCT and SS-OCT deliver real time A-scans and therefore output real-time B-scan images only. En-face images can be obtained in SD-OCT only after a whole high-density volumetric data is acquired, via a post-acquisition process only. In a first step, a series of B-scan OCT images is taken at different transverse coordinates to sample the whole volume, followed in a second step by sectioning the 3D volume to generate an en-face image. Therefore, a major disadvantage of SD-OCT systems is that they cannot produce en-face images in real-time. The time to produce an en-face image is determined by the time required to collect all volume data plus the time needed to post-process the acquired data [16,17]. This involves several steps, data re-sampling, numerical spectral shaping, zero padding, Fourier transformation, etc. To speed up the process, graphic processor cards  and field-programmable gate arrays  have been reported, however, these raise the cost of the whole measuring or imaging system.
An alternative solution was proposed , where the amplitude of a single frequency band is extracted from the photo-detected signal while tuning the optical frequency of the optical source, by mixing the photo-detected signal with a reference signal of a particular chosen frequency delivered by a local oscillator. An en-face image contains points at the same axial position. This means that for these points, the same modulation of the channelled spectrum is produced. Points at the same depth value produce the same number of peaks in the channelled spectrum and so when the channelled spectrum is read by tuning the optical frequency, a particular frequency is obtained for the pulsation of the photo-detected signal. However, this method is only applicable to SS-OCT systems using Fourier domain mode-locked swept laser sources, which provide a highly linear dependence between optical frequency and time sweep . The use of this method in any other SS-OCT systems requires re-sampling of data. This method presents also the disadvantage that supplementary modulation of the swept source is needed to ensure a Gaussian profile for the final coherence gate. If more en-face images are required from more depths, then more filters or mixers need to be assembled in the digital interface. To produce a new en-face image at a different depth, the volume of data needs to be read along the axial coordinate to produce the modulation corresponding to the depth wherefrom an en-face image is to be inferred from. If the calibration is imperfect, then the amplitude of the signal and the brightness in the image are lower.
Here, we introduce a new class of spectral domain interferometry set-ups, made from two interferometers, a Master Interferometer (MI) and a Slave Interferometer (SI). Such a set-up operates like a time domain interferometer, providing signal from a single point in depth only, however with the sensitivity of a SD method. By replacing the Master Interferometer with a storage bank of channelled spectrum shapes, where the storage delivers a similar signal to that previously delivered by the Master Interferometer, this time by reading a memory, we regain the advantage of SDI, of interrogating several depths in one process. The MSI procedure is however radically different than the conventional SDI, as points from the A-scan reflectivity profile are delivered in parallel, their number being equal to that of memories stored.
Our method, not being based on FFT, does not require linearization of data for sensing applications. In addition, when applied to OCT, this method allows speeding up the image presentation and simplifies the hardware.
Principle of operation of the MSI method
As shown in Fig. 1(a), the MSI principle employs a configuration of two interferometers, Slave and Master, where a Slave Interferometer (SI) “listens” to the operation of a Master Interferometer (MI). The SI and MI interferometers as illustrated here are Michelson interferometers, consisting in a master beam-splitter (MBS), a slave beam-splitter (SBS), a master reference mirror (MRM), a slave reference mirror (SRM) and an object (O), placed in the object arm of the SI whilst a master object mirror (MOM) is used in the corresponding arm of the MI. More specifically, signal is acquired by the Slave Interferometer on the right, for an OPD value determined by the Master Interferometer, on the left. In the Master Interferometer, the OPDmaster is determined by the difference between the optical path lengths measured from the master beam-splitter (MBS) to the two mirrors, master reference mirror (MRM) and master object mirror (MOM). In the Slave Interferometer, the OPDslave is determined by the difference between the reference path length (measured from the slave beam-splitter (SBS) to the slave reference mirror (SRM)) and the object path length (measured from SBS to different scattering points in the object, O).
The MSI method, implemented by the generic blocks in Fig. 1(a) is applicable to all types of SDI methods. The two interferometers may operate according to one of the spectral domain interferometry principles : (i) spectrometer based (Sp) [1, 2, 22], in which case the optical source, (OS) is broadband and the master acquisition block (MAB) and the slave acquisition block (SAB) consist in spectrometers, made for instance of a linear camera behind a prism or a diffraction grating; (ii) swept source (SS) based, in which case the OS is a tunable narrow band laser and the MAB and SAB consist in photo-detectors [3, 4, 23]. The channelled spectrum delivered by the MI, M(OPDmaster) and the channelled spectrum CS(OPDslave) delivered by the SI are compared in a comparison block C. The better the similarity of the two channelled spectra, the larger the amplitude of the signal A delivered by C.
At the core of the method presented here is the comparison block, C. This compares the channelled spectrum of the master interferometer, M(OPDmaster), with the channelled spectrum at the output of the slave interferometer, CS(OPDslave). When the two patterns are similar (i.e. when the number of peaks and troughs in the channelled spectra delivered by the two interferometers is the same), the comparison block C delivers a maximum signal. The more different the two patterns are, less is the amplitude of the output signal delivered by the comparison block. In this paper, correlation is used to implement the comparison method. Channelled spectra of different periodicities are produced at the output of the Slave Interferometer due to scattering points at different axial positions in the object O. Out of these channelled spectra, maximum signal will be delivered by the comparison block C for that channelled spectrum whose shape corresponds to the OPD value selected in the MI, i.e. for the OPDslave = OPDmaster. By modifying the OPDmaster (achieved by moving the MRM to a different position), signals from different depths inside the object O can be selected, one such signal at a time, like in time domain interferometry.
The principle of operation described above for the MSI method is different from that currently used in SDI and presents some unique properties, which are detailed below. In conventional SDI, the processing in the SAB is based on FFT or on other equivalent transformations [24–26] of the photo-detected signal delivered by the line cameras in a Sp-SDI or delivered by the photo-detectors in SS-SDI. Such transformations of the photo-detected signal deliver an A-scan from the object O. An A-scan represents a reflectivity profile from inside O, which displays the reflectivities of a succession of scattering points in depth, according to their distance up to SBS. Reflectivities of all scattering points within the A-scan are delivered in one FFT process .
The Master Interferometer on the right in Fig. 1(a) can be replicated to deliver more than a single depth information. A number P of such MIs can be installed for the same number of values of OPDmaster from P depths. In order to compete with the conventional SD technique, the minimum number P of Master Interferometers should be larger than the number obtained by dividing the axial range with the axial resolution.
Instead of replicating the Master Interferometer by P in Fig. 1(a), a more practical set-up is shown in Fig. 1(b). Essential for the operation of the P number of comparison blocks (correlators) is the set of signals delivered by the P Master Interferometers. These signals represent the shapes of channelled spectra corresponding to P different OPDmaster = OPDp, with p = 1,2,…P values in the Master Interferometers. The channelled spectra for the P number of OPDp values can be sequentially measured using a single interferometer and stored in memories M(p), placed in a storage of memories (SoM), which can be subsequently read during the measurement process. This leads to an alternative arrangement to that in Fig. 1(a), where the P Master Interferometers are replaced with the SoM, with P memories in Fig. 1(b). When reading each memory M(p), the SoM in Fig. 1(b) delivers a similar signal to that previously delivered by the Master Interferometer for the OPDp in Fig. 1(a). Here, the role of the Master Interferometer is accomplished by the Slave Interferometer itself, used in two stages, in a 1st stage to generate stored versions of channelled spectra and in a 2nd stage, for the measurement of signals from depths in the object O corresponding to unknown OPD values. In the 1st stage, the mirrors of the XYSH are held at rest and the procedure starts with a mirror as object placed in the slave (and single) interferometer. At this stage, the interferometer performs the function of the MI in Fig. 1(a). A number of P OPD values (OPD1, OPD2,…OPDp, … OPDP) are created by placing the SRM in P positions and P channelled spectra, M(p) are recorded into the SoM. After the storage of the P channelled spectra, the interferometer is used in the 2nd stage, measurement, where the unknown object, O, replaces the mirror used in the 1st stage. In this 2nd stage, parallel processing is performed, where each comparison block Cp compares (correlates) the shape of the current channelled spectrum, CS(OPDslave) = CS(OPD), delivered by the SAB with the pth stored version of the priori acquired and stored channelled spectrum, M(p). In this way, the MSI method delivers parallel readings of P OPDp values, which reinstates the high-speed acquisition characteristic specific to conventional SDI. Whilst in conventional SDI, all the OPDs along the depth were interrogated at once in a signal delivering the A-scan along a single line, the MSI method delivers several P points of the same A-scan reflectivity profile in parallel along several lines. Comparison blocks C1, C2, …Cp, …CP perform in parallel the operation of comparing the current channelled spectrum delivered by the interferometer with the P stored versions of channelled spectra (memories): M1, M2,…Mp,…MP. Each comparison block delivers a signal of amplitude Ap proportional to the interference signal due to the corresponding OPDp in the interferometer. The amplitudes A1, A2,…Ap,…AP provided in parallel, are practically sampled points of the same A-scan delivered by the conventional SDI.
Materials and methods
As OS, a swept source (Axsun Technologies, Billerica, MA), central wavelength 1060 nm, sweeping range 106 nm (quoted at 10 dB) and 100 kHz line rate is used. Instead of SBS, the interferometer configuration uses two single mode directional couplers, DC1 and DC2. DC1 has a ratio of 20/80 and DC2 is a balanced splitter, 50/50. DC2 feeds a balance detection receiver from (Thorlabs, Newton, New Jersey, model PDB460C), using two photo-detectors, PhD1 and PhD2 and a differential amplifier DA. 20% from the OS power is launched towards the object arm, via lens L1 (focal length 15 mm), which collimates the beam towards a pair of scanners XYSH, (Cambridge Technology, Bedford, MA, model 6115) followed by an interface optics made from two lenses, L2 and L3, (both of 75 mm focal length). The power to the object O is 2.2 mW, where the object O is shown either as the retina of an eye or mirror, paper or skin, as detailed below, in a model eye, MO, using lens L4 (focal length 22 mm).
At the other output of DC1, 80% from the OS power is directed towards the reference arm equipped with slave reference mirrors, SRM1, SRM2, placed on a translation stage, TS to adjust the OPD in the interferometer. As TS, a linear actuator (Newport, Irvine, CA, model UE404CC), 1 µm resolution was used, controlled by a Newport driver MM4005. Collimating lenses L5 and L6 are similar to L1. The signal from the balanced receiver is sent to one of the two inputs of a dual input digitizer (Alazartech, Quebec, Canada, model ATS9350, 500 MB/s). Its second input is used for the clock signal delivered by the Axsun source, shown as dashed line, as it is not necessary for the MSI method. A trigger signal from the OS synchronizes the acquisition (input T). The personal computer PC implements the comparison operation via correlation, stores the memories, Mp, acting as MI and performs the display of OCT images. In dashed line, an FFT block is also shown, to perform conventional signal processing of the acquired channelled spectrum CS(OPD).
The amplitude of the signal originating from a certain depth in the object is obtained following the steps described in the two equations below:
- 1. Correlation of the current channelled spectrum, CS(OPD) with a stored version of the channelled spectrum measured for an OPDp, provided by the memory cell Mp in the the SoM, Mp = M(OPDp), is obtained as:
where symbol signifies the correlation operation. The correlation is evaluated over the optical spectrum, with summation variable the wavenumber, k. If the line-width of the swept source spectrum in Fig. 1 and Fig. 2 determines a number of pixels M in sampling the optical spectrum at the interferometer output, the summation of products of the two terms is performed over 2M + 1 points. For the data in Fig. 2, 2M + 1 = 2561 points.
We have devised dedicated software to acquire and manipulate data. This was implemented using Labview 2012, 64 bit, from National Instruments. Two programs were created, progFFT and progCorr. They have a common coding core that acquires and digitizes data via the Alazartech digitizer. Data digitization can be performed under the control of an external clock signal provided by the Axsun swept source or by an internal clock signal.
Practical illustration of the MSI method
First, interferometry functionality is demonstrated, by keeping the scanning head SHXY at rest. Let us evaluate the effect of the window, W, around the wavenumber k of zero value (Eq. (2), on the axial resolution of the MSI set-up. This window can be conveniently used to define the depth resolution of the system, as an unique feature of the MSI method. Using the model object, MO, equipped with a mirror, the OPD values were adjusted in 64 positions, symmetric, around an OPD value of 0.5 mm, using the translation stage TS, controlled in steps of 1 μm. P = 64 channelled spectra were collected and stored as memories M(p). The smaller the window width value, the narrower the profile of the output signal versus OPD and the better the axial resolution achieved. This effect is demonstrated in Fig. 3(a), where the depth resolution of the system was measured as a function of the window size applied to the correlation signal. The depth resolution is determined here as the full width half maximum (FWHM) of the profile of 64 amplitudes obtained according to Eq. (1) by correlating the channeled spectrum acquired with the 64 memories, covering an axial extension of 64 μm. For a narrow window size, W, of less than 10 points, a depth resolution as small as 10 µm could be achieved.
The widow W can also be used to adjust the sensitivity of the MSI method. The sensitivity of the both methods was measured by first adjusting the reference arm signal, such that the spectrum at the photo-detectors was near to their saturation value. Then a neutral density filter, characterized by an optical density OD = 2 was placed into the sample arm. The sensitivity was calculated using the following equations, according to similar procedures described in [27, 29].
For the correlation based MSI method, the sensitivity is calculated as:
The number 40 in the two equations above is due to the neutral density filter. The MSI method delivers signal from a single OPD value only, at any given time, therefore it may look similar to the time domain interferometry case and en-face time domain OCT case. However, the signal is delivered here based on a spectral domain principle and therefore, the MSI method exhibits better signal to noise ratio and sensitivity than time domain interferometry, while providing signal from a single depth. To perform such functionality of selecting signal from a single depth only, the set-up in Fig. 1(a) can be used or the set-up in Fig. 1(b) using a single memory and a single comparison block.
The dependence of the MSI sensitivity to the window width W is shown in Fig. 3(b) by the red solid curve, while the value of the sensitivity for the conventional FFT based SDI method is illustrated by the blue dashed curve. As expected, the sensitivity increases with the width of the window W. For W larger than 40 points, the sensitivity becomes larger than its corresponding value calculated using the FFT method.
The MSI sensitivity curve exhibits a maximum at W = 320. The sensitivity does not increase monotonically with W, due to the fact that at high frequencies, the correlated signal draws little signal contributions from the sample. Therefore, a good choice for W is W = 80-100 points, where the depth resolution is ~12 - 14 µm, close to the calculated value (10 µm), and where the sensitivity is comparable to that of the conventional FFT based SDI.
In the conventional FFT based SDI, the axial resolution is determined by the FWHM of the A-scan of a mirror. To demonstrate that the MSI method is immune to non-calibrated data, A-scans for both calibrated and non-calibrated channelled spectra are produced using a mirror as object, by FFT and by the MSI method in Fig. 4(a) and 4(b). Again, using the model object, MO, equipped with a mirror, the OPD values were adjusted in 64 positions, symmetric, around an OPD value of 1.28 mm, using the translation stage TS, controlled in steps of 1 μm. P = 64 channelled spectra were collected and stored as memories M(p). When the FFT method is used, it is expected that the depth resolution depends on the quality of the clock signal used for calibration .
A depth resolution as small as 21 µm is achieved when using the external k-clock (blue dashed curve in Fig. 4(a)), which can be as large as 106 µm when no re-sampling is performed (blue dashed curve in Fig. 4(b)). On the other hand, the correlation based MSI method is completely immune to the way in which data are sampled, the depth resolution in both situations demonstrated in Fig. 4(a) and 4(b) is the same, 14 µm. A window W = 100 was used, where sensitivity of the two methods is similar, according to Fig. 3(b). These measurements show that better depth resolution is achievable using the correlation based MSI method than using the FFT based SDI traditional method. The slightly lower resolution achieved by the FFT based SDI in Fig. 4(a) may be due to dispersion left uncompensated in the system or due to imperfections in the clock provided by the swept source. Figure 3(a) suggests that even better axial resolution would be achievable by reducing the window W and trading off sensitivity.
The sensitivity drop-off of the MSI method was also evaluated experimentally. The channelled spectrum was acquired and processed using the traditional FFT method and results were compared with those obtained using the MSI method, by correlating the current channelled spectrum with 8 stored versions of channelled spectra priori acquired. In order to obtain the stored versions of the channelled spectrum, the XYSH was kept at rest and channelled spectra were recorded and retained in 8 memories, for 8 OPD values distributed from 0.25 mm to 3.5 mm measured in air. In Fig. 5, the sensitivity drop-off measured using the FFT method is shown (blue dashed curve) as well as the sensitivity profiles obtained using the MSI method (red curve) for three values of the window width, W: 10 (for which, according to Fig. 3(a) the best value of the depth resolution is achieved), 100 (for which, according to Fig. 3(b) sensitivity values similar to those obtained using the FFT method should be achieved) and 320 (which will provide the best sensitivity).
As it can be noticed in Fig. 5, the shape of the sensitivity profiles are quite similar, proving that the MSI method can be used to measure the strength of signal backscattered from points at different depths. Similar roll-offs of around 5-6 dB per 3.5 mm were obtained in all four cases. A number of 10 measurements of the sensitivity profiles were performed over a 10 hours time interval and variations less than 1 dB were recorded on all points.
MSI generation of en-face OCT images and comparison of such images with those delivered by conventional SD-OCT
In top of the functionality of MSI demonstrated above, OCT operation is demonstrated by using the 2D scanner, the XYSH, in the object path. The MSI based OCT operation is illustrated by acquiring several en-face images from the eye and skin.
The core of the Labview programs was completed with the necessary code to drive the galvo-scanners XYSH (using a DAQ board from National Instruments, model 6071E) and also to feed the Alazartech board with a TTL signal to determine the number of A-scans per each T-scan line in the en-face image.
To produce an en-face image using the conventional SDI technique, after acquisition and digitization, A-scans corresponding to each sweep were produced using the progFFT, which implemented FFT. For benchmarking purposes, data were resampled using a cubic spline interpolation prior to FFT. The volumetric data corresponding to the 40,000 A-scans was then software cut to produce an en-face OCT image at the depth required.
To produce an en-face image using progCorr, no resampling of data, FFTs or software cutting were performed. Instead, correlations between the stored shapes of channelled spectra in the SoM and the currently measured channelled spectrum, CS(OPD), were calculated using the MSI procedure described above.
In the 1st stage, P = 64 memories are created with 64 channelled spectra for OPD values separated by 30 μm, using the translation stage TS and the model objet, MO, using a mirror as object O. In the 2nd stage, the set-up is used to acquire a scan frame from the object. To avoid the effect of movement, the en-face OCT image size was limited to 200x200 pixels, to be able to complete a volume acquired in 0.4 s. The finger and the optic nerve were placed slightly away from OPD = 0 to avoid mirror terms disturbing the images. Therefore, many images from OPD = 0 until the coherence gate intersects the object show nothing, so this is why only the last 48 en-face OCT images are presented in Fig. 6 and the last 36 images in Fig. 7.
As P signals are delivered in parallel corresponding to P OPD values, P en-face OCT images can be delivered directly and simultaneously. In this way, no software cuts are needed as in conventional SD-OCT. In other words, the MSI method shifts the bottleneck of signal processing from processing of A-scans, to implementing P parallel comparison operations (correlations). For each set of coordinates of the lateral pixels (i,j) from the set of (200, 200), the conventional SD-OCT method delivers all points in depth along the A-scan starting from pixel (i,j), in a single electrical signal. More advantageously, the MSI method delivers the intensities of P points in the same A-scan along P electrical signals, in parallel. In other words, there is no need to separate the A-scan into samples corresponding to different depths (as the conventional SDI requires), the MSI configuration delivers such samples along separate outputs and the only requirement is to assemble the en-face images. Therefore, by the end of a complete frame performed by the scanning head SHXY, P en-face OCT images can be quicker produced, using signals from P separate comparison blocks, a block for each depth, as shown in Fig. 6(a) and 7(a).
The two methods, conventional SDI and MSI are equivalent in completing acquisition of the same 3D volume, however if en-face views are needed, the conventional SD-OCT method requires time for software cuts of the 3D volume at constant depths, let alone the need for calibration and linearization of data. For comparison, images created using the conventional SS-OCT method are shown in Fig. 6(b) and 7(b). The images obtained by applying the MSI method and shown in Fig. 6(a) and 7(a) are similar to those produced by the conventional technique in Fig. 6(b) and 7(b). However, the MSI method tolerates better occasional saturation in the object path. To produce the images using the conventional FFT based SDI, deduction of an average image from all B-scans is used to reduce the noise, according to normal practice . This method however creates saturation lines in the images where there is a strong reflectivity signal, as visible in Fig. 7(b). The correlation based MSI method is immune to this phenomenon, as another advantage of the MSI method. The images in Fig. 7(a) are free from this pattern noise.
For a 200x200 pixels in transversal section, 40,000 channelled spectra are collected. We used this number to evaluate comparatively the time required by the conventional SDI method, based on FFT and linearization and the MSI method presented here, when employing an Intel® Xeon® CPU, model E5646 (clock speed 2.4 GHz, 6 cores). An FFT operation requires as little as 2.825 µs while correlation based on multiplication and integration takes up to 9.2 µs. If linearization of data is needed, then an A-scan is obtained in 7.2 ms.
Correlation can also be implemented using three FFTs . By storing FFTs of the channelled spectra, only two more FFTs are needed to perform the correlation. Performing two FFTs to implement correlation is obviously longer than a single FFT, but much shorter than the time required for linearization plus FFT in the current SDI technology. This determines a net advantage of the MSI method presented here in terms of time, let alone the advantage in terms of hardware by eliminating the need of linearization and calibration.
The one frame volume was acquired in 0.4 s. Then, the production of each en-face image using the MSI method based on 2 FFTs takes 368 ms. Adopting a parallel computing strategy based on graphics cards and CUDA would reduce the time to produce P such en-face OCT images to the time to produce a single OCT image. Such a drastic reduction of overall processing time is not achievable using the conventional SDI technique, let alone the provision of en-face images.
On the same computer, the production of an en-face image using the FFT method takes 334 ms. However if re-sampling of data is required prior to FFT, the time required to generate an en-face image using the FFT technique is much larger, over 3.5 s.
The MSI method requires a complete frame to be scanned, which here took 0.4 s for 200 x200 pixels. Therefore the MSI method is ideally suited for high speed SD-OCT which can capture substantial volumes in subsecond time. Over 1 MHz line rate  is now achievable. Using such a scanning rate, the same volume would have been captured in 40 ms. Alternatively, the number of lateral pixels in the volume can be increased while still achieving sub-second volume scanning.
The method presents net advantages in comparison with the classical method of producing axial reflectivity profiles in spectral domain interferometry by FFT or any other similar transformations. These advantages refer to: (i) no need for resampling of data; (ii) tolerance to dispersion; (iii) possibility to tailor the depth resolution; (iv) enhanced signal to noise ratio, less artifacts due to occasional strong signal, plus enhanced versatility in 3D presentation of results as en-face cuts are produced directly and in parallel. In terms of dispersion, not only that the MSI method tolerates dispersion in the configuration, but in principle, can also be tailored to tolerate dispersion due to the object if the collection of channeled spectra to be stored as memories determined by the master interferometer, are collected by keeping the MRM and MOM fixed in Fig. 1(a) (or equivalently the SRM and the mirror replacing the object in the 1st stage of capturing the channeled spectra M(p) to be stored in Fig. 1(b)) and using slabs of the same material as that of the object to achieve different OPDmaster values.
Because the signal processing is based on comparing channelled spectra (correlating) them, there is no need to organize the data delivered by SDI in equal frequency slots. Even more, chirped (non regular) patterns of channelled spectra due to dispersion are tolerated, as the chirped channelled spectrum delivered by the Slave Interferometer is compared with the same-channelled spectrum shape delivered in the prior measurement stage, and incorporated into the SoM. The MSI method is not only more tolerant to dispersion, but requires less time for processing, as there is no need for zero padding, interpolation and calibration, as otherwise required by conventional SDI  before performing FFT.
The novel MSI method presented here does not need calibration, and therefore its results are not dependent on the quality of data linearization. It is known that the linearization methods, whatever complex, cannot accurately organize the data in equal frequency slots. Therefore the MSI method can reduce the cost of instruments performing measurements of distances and the cost of OCT systems, by eliminating the need for hardware components to linearize data from spectrometers (when using Sp-SDI) or from photo-detectors (when using SS-SDI). There is no need of optical prisms in Sp-SDI and no need for special optics and electronics to deliver a linear clock in SS-SDI. In case linearization was done in software, there is no need for powerful multicore computers with the added advantage of time, as no extra procedure (linearization) is needed.
The MSI method is easy to implement. It can be incorporated into any existing spectral domain sensing system or into any existing OCT set-up, with no modification to the hardware. Only the construction of an electrical correlator is required, which can be done on the same digital platform used to process the signal from the spectrometer or from the photo-detector.
The MSI method bridges the gap between time domain and spectral domain OCT. Only time domain OCT can deliver an en-face OCT image in real time. The set-up presented in Fig. 1(a) implements spectral domain interferometry but delivers signal from a selected depth only, like a time domain interferometer. The advantage of spectral domain interferometry, of interrogating all OPD values at the same time is restored in Fig. 1(b) by parallel processing, where any number of en-face OCT images can be generated if the same number of shapes of channelled spectra was recorded a priori in a storage. By accessing all such shapes in parallel for comparison with the current channelled spectrum delivered by the spectral interferometer, superior processing speeds are achievable, of advantage for 3D volume generation.
This paper focused on production of en-face images. However, the MSI method can equally be used to generate B-scan OCT images. Let us say that the transversal scanner in Fig. 1 executes line scanning only. In this case, for each pixel along the transversal line scanned, the P correlators will deliver P points of A-scans which can be used to assemble a B-scan. The main difference is that the conventional SD-OCT method delivers an A-scan via a single electrical signal output, while the MSI method provides in parallel, sampled values of the same A-scan along several electrical outputs, as many as the P number of comparison (correlator) channels. The parallel provision of reflectivities from P depths confers the MSI method superiority in terms of en-face OCT image generation. The MSI method presents the advantage of not needing any calibration, however the time to create a B-scan using the MSI method is longer than the time required by the conventional method, as a correlation operation requires longer time than a Fourier transformation.
A correlation procedure can be implemented by three FFT processes, so it is slower than FFT. Performing several correlations, P, will slow even more down the production of images. However, this disadvantage may be addressed by parallel processing. More research is required to engage parallel-processing procedures to make full use of the avenues opened by the MSI method. Due to its parallel nature, the MSI method presents a net advantage in terms of en-face imaging as the processing block can provide in parallel signals for each depth for which a memory was created. Further studies are necessary to exploit this advantage in practice together with the use of graphic cards or field-programmable gate arrays.
The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme, Advanced Grant agreement 'COGATIMABIO', No: 249889. A. Podoleanu is also supported by the NIHR Biomedical Research Centre at Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology. The authors also appreciate the valuable advice on the manuscript received from Prof. Elizabeth Mansfield and Dr. James Bloor, both with the University of Kent.
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