Sensitivity versus depth
When employing TD principles, the same sensitivity is achievable for any OPD value, i.e. for any axial position of the scattering point along the A-scan, as shown at the bottom of . In opposition, there is a decay of sensitivity of the SD methods with the OPD, as shown at the bottom of and . Both SB and SS methods require resolution in separating the channelled spectrum peaks and troughs, which translates into the need of large number of grating lines, N, and large number of pixel cameras, M, when using the SB-OCT method and of a narrow linewidth, δλ, for the SS used in the SS-OCT method. In fact, fundamental in limiting the axial range in both types of SD methods is the spatial extension of the interfering wavestrains, CL. This can be assimilated to an equivalent coherence length, hence the notation. In the SB, CL is given by the extension of the object and reference wavetrains after suffering dispersion (or diffraction) in the spectrometer. It should be noted that CL is much larger than the coherence length cl introduced above. In the SS-OCT case, the spatial extension, CL, of the wavetrains emitted by the swept source, is inverse proportional to the linewidth, δλ, of the instantaneas spectrum emitted.
illustrates the spatial relativity of dimensions. The Object to be investigated is made of layers separated by δz and the OPD axial extension of the object is 2Δz (considering for simplicity the index of refraction as 1). In TD-OCT, the coherence length, cl, of the optical source needs to be smaller than δz to be able to separate the layers in depth in the object, as shown in . Because TD-OCT operates around OPD = 0, by moving the Reference Mirror in the interferometer in , maximum of sensitivity is moved from one layer in to the next. Therefore, all layers can be interrogated by the same sensitivity. This is not the case in SD-OCT.
To ensure interference of the local reference wave with both the waves coming from the top of the object as well as with the waves returned from the deepest layer, their spatial extension, CL, needs to exceed the OPD axial range 2Δz, CL > 2Δz as shown in . Let us say that the Reference mirror is adjusted for OPD = 0 to match the top of the Object. As illustrated in , total overlap of interfering wavetrains, object and reference, happens at OPD = 0 only, whereas for the maximum depth, tails only of object and reference wavetrains are superposed. The sensitivity depends on the amount of overlap of the two interfering wavetrains, object and reference, therefore, the sensitivity in SD-OCT decays with depth. However, because the wavetrains are longer than the axial range, 2Δz, they will all interfere to some extent with the reference wavetrain. In this way, all OPD values within the axial range 2Δz are interrogated at once. At any particular time, for any given optical frequency of the SS, wavetrains from all depths are returned back to the photodetector.
SD-OCT: Relative size of the CL extension of interfering wavetrains, required depth resolution δz, and axial range Δz determined by the axial extension of the Object to be investigated.
The wavetrain from the bottom of the object is shown with more cycles than the wavetrain from the top of the object, as the picture in represents a frozen aspect in time of returning wavetrains from the top and bottom of the object. (For clarity, the wavetrains from the top and bottom of the object are shown only and they are also displaced relative vertically, otherwise they should be in line, like in , and superposed.) Because of the frequency tuning, by the time the emitted wavetrain from the SS reaches the bottom of the object, the frequency of the wavetrains reaching the top of the object has changed. This difference in frequency will give the pulsation of the beating signal resulting from the interference of the object and reference wavetrains at the Photodetector. In this way, the axial position of scattering points along an A-scan in depth within the object is encoded on the frequency of the beating signal, with a linear proportionally between the frequency of the beating signal and the OPD value of scattering points.
In the case of the SB-OCT, the interfering waves are those after passing through a disperser, a prism or a diffraction grating. Their equivalent coherence length is elongated by dispersion/diffraction to CL. For instance, for a beam extending over N
grating lines, the wavetrain length, CL in the first order of diffraction is Nλ
. To cover an object of axial extension Δz
, for the reasons explained earlier, Nλ
needs to be larger than Δz
. A second condition originates in the need that the camera in the spectrometer has sufficient number of M
pixels to resolve the channelled spectrum. The number of cycles in the channelled spectrum is given approximately by the OPD/cl, where the coherence length, cl, can be approximated by
To resolve the largest number of peaks in the channelled spectrum, corresponding to the maximum axial range, where OPD = 2Δz
, and considering that two pixels are necessary to resolve a complete cycle of the Photodetector
signal, the minimum number of pixels, M
, on the camera needs to be:
This is equivalent to requiring that the spectral width projected on each pixel, δλ, be shorter than half of the spectral distance
between adjacent peaks in the channelled spectrum for any given OPD (as illustrated in ). For the maximum axial range, OPD = 2Δz
, this condition becomes:
as commented above.
Similar conditions hold for SS-OCT, where δλ is the laser linewidth and M is the number of minimum equivalent steps within the tuning bandwidth, Δλ=Mδλ/2. The division by 2 considers that at least two steps in the wavelength change per cycle in the channelled spectrum are required for proper sampling of the channelled spectrum.
In TD-OCT, for each position of the coherence gate, the two wavetrains overlap entirely, over all their cl extension (). In SD-OCT, the wavetrains overlap entirely over all their CL extension for OPD = 0 only, whereas for an increasing OPD value, their overlap reduces (). This explains why the sensitivity is constant with OPD in TD-OCT whilst it decays with OPD in SD-OCT as illustrated by the dashed curved at the bottom of and . To ensure a long CL and hence a large axial range 2Δz, in SB-OCT, a large number of grating lines, N (and a large number of pixels M to sample the channelled spectrum in the array) are required, whereas in SS-OCT, a linewidth, δλ, as narrow as possible is needed.
Let us say that the spectrum of width Δλ spread over the linear camera in the spectrometer in the SB-OCT is read in a time, T. Equivalently, the frequency of the tuneable source in the SS-OCT is tuned within a spectrum of width Δλ in time, T. Then the frequency, f, of the signal at the output of Processing unit during either by reading the camera in SB-OCT in or by tuning the laser in SS-OCT in is: f= (1/T)(OPD/cl) where cl is the coherence length evaluated for the broadband spectrum Δλ in SB-OCT and evaluated for the tuning bandwidth Δλ in SS-OCT.
Time to produce an en face C-scan slice and time to collect a volume
SB-OCT and SS-OCT setups output A-scans, therefore they cannot produce a 2D en face
map (C-scan) image in real time. C-scan sections can be obtained in SB-OCT and SS-OCT only after a whole volume of the Object
is acquired, i.e. via a postacquisition 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 so generated to slice a C-scan. Therefore, in SD-OCT, the time to produce a C-scan is determined by the time required to collect all volume data plus the time taken by the software cut. Recent progress in SS-OCT has lead to multi MHz A-scan line rates (Klein et al., 2011
). A 5 MHz line rate for instance allows a B-scan image of 500 lines to be created in 0.1 ms. If 500 such frames of 500 pixels in depth in the A-scan are acquired, this means a volume of 5003
of pixel data captured in approximately 0.05 s (). This represents the minimum time interval to acquire the data necessary to produce a C-scan image. The time interval necessary to practically produce a C-scan image is larger, as extra time is required for the software cut to sample the corresponding slice from the data volume. This shows the connection between the number of voxels acquired in the unit of time and the time taken before a C-scan image can be produced. Maximum acquisition speed in en face
OCT is achievable using a resonant scanner at 16 kHz, in this case, a C-scan image of 500 lines can be created in 32 ms. Therefore, when compared with the 50 m-s above, en face
TD-OCT can create a C-scan image slightly faster than the fastest SS-OCT systems reported so far. However, for a similar volume made of 500 pixels along 500 T-scans per C-scan in 500 C-scan frames, en face
OCT requires 15.5 s, much longer than 50 ms taken by SS-OCT. Therefore, modern SS-OCT technology can create a volume with less movement artefacts than the TD-OCT technology. Multi MHz line rates coupled with parallel scanning can lead to even faster OCT rates in producing meaningful data volumes, as for instance in (Wieser et al., 2010
) where a 5.4 MHz line rate with four simultaneous beams allowed collection of 4.5 GVoxels/s data.