1. Introduction

Optical coherence tomography (OCT) is an emerging biomedical imaging technique that generates in vivo cross-sectional images of tissue microstructure with micron-scale spatial resolution [1]. OCT measures the echo time delay of backscattered and backreflected optical signals from different layers within a biological tissue specimen, typically by using a fiber optic Michelson interferometer and a broadband light source. Standard OCT systems generate images by analyzing only the intensity of the backscattered light, and are therefore limited to providing structural information about the tissue sample based on the amount of light backscattered by the various tissue structures. Therefore, this technique does not allow investigation of the spectroscopic properties of the tissue sample. Analysis of spectroscopic features can enhance the contrast of OCT systems by differentiating tissue based on properties other than the intensity of the backscattered light, such as the center wavelength of the detected spectrum at each pixel in the image [2]. Spectroscopic contrast enhancement is possible when two tissue or material types in a sample backscatter the same amount of light, but with different distributions over the wavelength range of the OCT light source. In this case, standard intensity-based OCT would fail to differentiate the tissues or materials, but differentiation would be possible through spectroscopic analysis.

Two fundamental sources of spectroscopic contrast in OCT imaging are wavelength-dependant absorption and wavelength-dependant scattering. Endogenous or exogenous materials with characteristic absorption profiles such as melanin, hemoglobin, water, or contrast-enhancing dye can be used to provide spectroscopic contrast based on wavelength-dependant absorption. Recently, contrast enhancement using spectroscopic OCT with near-infrared dyes has been demonstrated in plant material [3] and developmental biology specimens [4]. Spectroscopic OCT systems have also been demonstrated that are capable of measuring wavelength-dependant absorption in blood samples to extract oxygenation levels in vitro [5]. Wavelength-dependant scattering properties provide an alternative source of spectroscopic contrast. In this case, spectroscopic contrast is based upon the fact that scattering particles of different size, refractive index, and spatial distribution produce backscattered spectra with a characteristic modulation of the spectrum.

Much work has been carried out in measuring the size of epithelial cell nuclei using light scattering spectroscopy to detect cancer cells in vivo and in vitro, as well as to characterize particle size using artificial microspheres and cellular monolayers [6–13]. Central to this work is idea that the cellular organelles of epithelial tissue can be considered as spheroidal scatterers whose interactions with light are governed by Mie theory [14,15]. Mie scattering theory provides a closed-form description of optical scattering from spheroidal particles as a function of particle size, refractive index, wavelength, observation angle, and optical polarization. Mie theory describes the scattering process in closed form for simple systems of spherical particles under coherent illumination. For single-particle systems, the frequency of the modulation on the backscattered spectrum is proportional to the particle size. The modulation characteristics of the backscattered spectrum are also related to the density of the scattering particles. Therefore, by examining the spectral modulations present in spectroscopic OCT signals, variations in the size and density of scattering particles in biological tissue samples may be differentiated. Since the cells that compose various types of tissue typically have varying organelle sizes and densities, examining spectral modulation may lead to contrast enhancement of different cell types. Furthermore, diseases such as cancer often cause changes in cell size, nuclear size, and mitochondrial density. Such changes may also be indirectly visible using spectroscopic OCT imaging.

In OCT systems, the signal detected at each point in the image is the result of backscattering by all of the particles within the imaging volume defined by the coherence length of the light source and the imaging beam diameter. A typical ultrahigh resolution OCT system may have a coherence length of 2 µm and a beam diameter of 5 µm, giving an imaging volume of ~39 μm³. When imaging biological specimens, many individual scattering particles such as mitochondria and cellular nuclei are present simultaneously within one imaging volume. This causes coherent interference between the scattered fields of each particle within the imaging volume. When the number of particles becomes large, the coherent interference between scattering particles causes the detected signal to become stochastic, creating speckle noise. In standard OCT systems, speckle noise is visible only in the intensity of the detected signal. In spectroscopic OCT systems, speckle noise is present in the intensity of the signal as well as in the backscattered spectrum, the distribution of the signal over wavelength.

In this paper, the development of a new spectroscopic OCT analysis technique based on a statistical analysis of local spectral modulation is described. Since the technique is intended for use in biological tissue imaging where the number of scattering particles contained in the imaging volume is large, the detected spectroscopic signal is assumed to be stochastic instead of deterministic. The detected spectra at each point in the image are therefore modeled as individual outcomes of random variables, where the statistical properties of the random variables are determined by the distribution of scattering particle sizes and particle number density within each imaging volume. To quantify the underlying random process that generates the optical spectrum at each image point, the autocorrelation function of the observed spectrum is used. Tissue areas with high spectral modulation produce autocorrelation functions that fall off rapidly away from the central point, while areas with low spectral modulation produce autocorrelation functions that fall off slowly. The bandwidth of the autocorrelation function is encoded in the hue of a hue/saturation/luminance (HSL) color map, while the intensity of the backscattered signal is encoded into saturation and luminance. In this way, contrast enhancement is provided based on the distribution of particle sizes as well as the intensity of the backscattered signal. Since this new spectroscopic analysis technique does not depend on the distribution of optical power over absolute wavelength, it is insensitive to major sources of spectroscopic noise.

This paper is organized as follows: First, we discuss an improved method of calculating the local optical spectra from the detected OCT signal using the Chirp Z Transform (CZT) [16] in a Short Time Fourier Transform (STFT) implementation. Next, we present a method for simultaneously encoding spectroscopic and intensity data into a HSL color map to combine the sharp intensity features of standard OCT imaging with the contrast enhancement capabilities of spectroscopic OCT. We then discuss sources of spectroscopic noise in OCT systems, and present the new spectroscopic analysis technique in detail. The concept is illustrated with experiments using polystyrene microspheres, and preliminary studies on developmental biology specimens are presented, illustrating that noise-insensitive contrast enhancement in vivo is possible with the new technique.

2. Spectroscopic OCT system and local spectrum calculation

Traditional OCT systems measure the envelope of the demodulated interference signal to produce two-dimensional maps of backreflected/backscattered light intensity. These maps provide information on tissue microstructure by characterizing the amount of light backscattered by the tissue at each point in the sample. Spectroscopic OCT data analysis is based on a time-frequency decomposition, such as a short time Fourier transform (STFT), of the interference fringes acquired during each A-scan. This requires the complete interference fringe to be acquired by the A/D card instead of just the demodulated envelope signal. Figure 1 shows a schematic of the spectroscopic OCT system used in this study. The system uses a Ti:sapphire laser with a center wavelength of 800 nm and a bandwidth of 200 nm, resulting in a coherence length of 1.9 µm in air. The beam diameter is ~5 µm, and the incident power on the sample is 2 mW. The galvanometer velocity v_g is 3.6 mm/s, giving an RF detection frequency of 9 kHz and a bandwidth of 4 kHz. Dual-balanced detection is used to reject amplitude noise in the laser source. The OCT signal is acquired without demodulation using a 16-bit A/D card operating at a sampling frequency of f_s=166 kHz, oversampling the OCT signal by a factor of ~7x.

Previous work in spectroscopic OCT has used an STFT approach to calculate local spectra at each pixel in the OCT image [2,3]. The “Morlet wavelet” method described by Morgner et al. [2] is actually not a multiresolution analysis or wavelet transform in the standard sense, but is equivalent to an STFT using a Gaussian window function. Compared to other time-frequency analysis methods, such as an actual wavelet transform, Fourier transform based approaches provide the most meaningful transformation from time- to frequency-domain. When the Fourier transform is used, there exists a direct mapping of RF frequency f_RF to optical wavelength λ_opt, given by

It is therefore easy to relate observations in the calculated optical spectra to physical phenomena, whereas in other time-frequency analyses, no direct mapping from the transform coordinate to optical wavelength exists.

 

Fig. 1. Schematic of spectroscopic OCT system. Dual balanced detection is used to reject amplitude noise in the Ti:sapphire laser. The reference mirror is scanned using a linear galvanometer. The detected signal is bandpass filtered, and the intereference fringes are acquired using a 16-bit A/D card.

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The basic element in the calculation of an STFT is the discrete Fourier transform (DFT). Although the DFT can be calculated very efficiently using the “fast Fourier transform” (FFT) class of algorithms, it suffers from a significant drawback when applied to spectroscopic OCT imaging. This drawback occurs because the FFT algorithm calculates the DFT over a fixed discrete frequency range of 0→2π, equivalent to 0→f_s in continuous frequencies, using L points. If the discrete RF spectrum of the interferometric OCT signal does not fill the entire range, the result is that unnecessary points in the transform are calculated, decreasing the efficiency of the algorithm. In other words, if the OCT system is not operating near the Nyquist sampling limit, then a FFT-based STFT will take longer than is necessary to produce spectra with a given number of points falling within a spectral band of interest. Since it is common for OCT systems to operate at sampling rates well above the Nyquist limit to reduce aliasing noise in the A/D converter, the fixed frequency span of the FFT-based STFT is inefficient.

To overcome the drawbacks of the FFT, in this study a chirp z transform (CZT) [16] is used instead of the FFT to compute the STFT’s used in the spectroscopic analysis. The CZT is a more general case of the DFT, where integration can be performed over an arbitrary curve in the z-plane instead of being limited to the unit circle. The L point CZT T of x[n] is given by

with z∈I. The choice of z controls the starting point of the transform, while the factor r controls the frequency resolution (and therefore the end point of the transform). By choosing $z=e^{-j{\omega }_0}$ and r=(ω ₁-ω ₀)/L, a DFT can be calculated from ω ₀→ω ₁ instead of 0→2π. In this case, the CZT gives

The number of points that fall within the range of interest ω ₀→ω ₁ can be increased by increasing L, but by using the CZT there will be no extraneous points calculated that fall outside the region of interest.

The frequency region of interest can be arbitrarily adjusted to match the OCT system’s optical bandwidth and A/D sampling rate. For the system used in this study, the optical wavelengths containing useful information fall between 600 nm and 1000 nm. From Eq. (1), the RF frequencies of interest therefore fall between 7.2 kHz and 12 kHz. After A/D conversion, these continuous RF frequencies are mapped into the discrete RF frequencies between ω ₀=0.087π rad/s and ω ₁=0.145π rad/s. Using an FFT algorithm with L=512 points to calculate the spectrum would result in a frequency spacing per point of π/256 rad/s, corresponding to ~15 points falling within the range ω ₀→ω ₁. Using a CZT of length L=512, all 512 points can be chosen to fall in the range ω ₀→ω ₁, giving a frequency spacing of ~π×10^-4 rad/s. This increased point density could be obtained using a standard FFT with zero-padding, but with a factor of 30 increase in the size of the transform required.

Figure 2 shows an STFT segment calculated from one A-scan of a Xenopus Laevis tadpole, using an FFT of length L=512 and a CZT of length L=512. The window function is a 512 point Hamming window, corresponding to 8.5 µm in tissue. For the CZT, ω ₀=0.087π and ω ₁=0.145π. For clarity, the x-axis values are converted back to continuous RF frequencies. Within the frequency range containing useful information, the CZT implementation produces a smoother spectrum than the FFT implementation. It should be noted that the additional points contained in the CZT are a form of oversampling in the frequency domain, and therefore do not contain any additional spectroscopic information compared to a standard FFT. However the CZT produces a smoother spectrum that is more suitable for further numerical analysis, while producing an equivalent spectrum with an FFT would require the unnecessary calculation of points lying outside of the frequency band of interest.

3. Visualization of spectroscopic information

Standard intensity-based OCT systems represent information about tissue backscattering as a grayscale or false color image. In these systems, the intensity of the backscattered light at each pixel in the image is stored as only a single value. By acquiring and processing the full interferometric OCT signal instead of only the envelope, it is possible to calculate a local spectrum for every pixel in the image using time-frequency analysis such as the short time Fourier transform (STFT) based on either the FFT or CZT. By generating an optical spectrum for every A-scan in a given OCT image, a 4-dimensional data set is produced, defined by transverse and axial coordinates as well as the wavelength and intensity of the detected light. For a human reader to interpret the information contained in the spectroscopic data set, it is necessary to first condense the data to three dimensions which are suitable for image display. This is done by choosing an appropriate spectroscopic metric (such as center wavelength) that quantifies the spectrum at each pixel with a single value. The development of a spectroscopic metric based on spectral modulation is discussed in more detail later. Here, we discuss the procedure for combining intensity and spectroscopic information together in a single color map to provide maximum tissue contrast.

 

Fig. 2. STFT segment from Xenopus Laevis tadpole, calculated using the CZT and FFT algorithms, each with 512 points. Data point density in the area of interest using the CZT is ~30 times higher than using the FFT. The FFT data set extends from -f_s/2 to +f_s/2, while the CZT data set extends only from 7.2 kHz–12 kHz.

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It is convenient and intuitive to use a color map to represent spectroscopic information, where the color can convey specific information about the spectra at each pixel. For this study, the Hue/Saturation/Luminance (HSL) color map was used as a starting point. The HSL map allows for independent adjustment of three values (H, S, and L) for every pixel. As H varies from 0 to 1, the color will vary from red to green to blue to violet and back to red. As S varies from 0 to 1, the color will vary from gray to fully saturated. As L varies from 0 to 1, the color will vary from dark to bright.

There are several possible ways to visualize spectroscopic OCT information. If the structural information relating to the intensity of the backscattered light is not important, then a pure spectral visualization technique is possible. In this case, the spectroscopic metric values for each pixel can be encoded into a grayscale map or arbitrary HSL map and displayed. In reality, this technique is not a good choice, since a better understanding of the tissue being imaged can be obtained by combining the intensity (structural) and spectral information into the same image.

When simultaneously displaying structural and spectroscopic information in an HSL color map, hue can be used to encode the spectroscopic information, and saturation and luminance to encode the intensity information. Previous work [2] used a fixed luminance value, encoding intensity information in saturation only. It is also possible to encode intensity information in saturation and luminance simultaneously. Better structural contrast and more vivid colors are obtained using the second method. In this study, a hue range of 0 to 0.6 is used to avoid wrapping of the map back to red. Saturation and luminance are equal, and range from 0 to 1.

To maintain the structural sharpness of standard OCT images, a hybrid visualization technique is used in this study. The spectral information (hue) was obtained from the local spectra, while the structural information (saturation and luminance) was obtained from the demodulated A-scans. First, a CZT-based STFT was calculated for each A-scan to generate local spectra for the extraction of hue data. Next, software-based Hilbert demodulation was applied to the raw A-scans and the value of the demodulated A-scan corresponding to the center of each STFT window was mapped into saturation and luminance values. The STFT window can be incrementally moved through each A-scan at arbitrarily small step sizes, regardless of the length of the window itself. In this way, the spatial resolution of the structural data is determined by the window step size while the spatial resolution of the spectral data is determined by the window length. The structural and spectral spatial resolutions are therefore decoupled and arbitrarily adjusted. Images processed in this manner have sharp intensity (structural) features, with blurring due to the STFT window effect limited to the pixel hue only.

4. Sources of spectroscopic noise

In order to design a spectroscopic metric that is insensitive to noise, it is necessary to understand the sources of spectroscopic noise in OCT systems. The first source is nonuniform reference path scanning motion, where nonlinearity in the motion of the optical path length scanner imparts a time-varying Doppler shift to the detected spectra. This Doppler shift can be removed by using a reference interferometer to trigger A/D conversion at evenly-spaced reference positions, at the cost of increased system complexity. It would therefore be more efficient to use a spectroscopic metric that is insensitive to Doppler shifts induced by small nonuniformities in the reference path scanner.

Another source of spectroscopic OCT noise is related to the broadband light source. When a solid-state laser is used as the OCT system light source, a broad optical spectrum is generated by femtosecond pulses. These pulses can be temporally chirped, such that the center wavelength of the incident spectrum varies over the pulse duration and therefore over the coherence length in the sample being imaged. This chirp can be removed for a single axial depth by adjusting the dispersion of the reference arm to match the dispersion of the sample at that point, but there is no way to maintain a chirp-free detected signal over the entire axial range of the image due to the dispersion of the materials in the sample. The effect is that when isolated reflecting or backscattering surfaces in the sample are imaged, the calculated spectra exhibit a chirp matching that of the incident pulse.

 

Fig. 3. Spectroscopic OCT image showing the center wavelength of the reflected spectrum from a mirror. Red colors indicate a comparatively long center wavelength, while green colors indicate a comparatively short center wavelength. The chirp of the incident pulse appears as a chirp in the detected spectrum, as shown by the depth-varying center wavelength. As the reference path dispersion is changed along the transverse coordinate, the chirp varies from short-long to long-short wavelength.

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Figure 3 illustrates the effect of a chirp when imaging a simple mirror in the sample arm. The chirp appears as a depth dependence in the center wavelength, with green colors indicating a shorter center wavelength and red colors indicating a longer center wavelength. As the image was acquired, the dispersion of the reference arm was varied, changing the dispersion matching between the reference and sample arms. Therefore at each transverse location, the detected signal has a slightly different chirp. The effect is that the center wavelength of the reflected spectra varies in the transverse direction, moving from short/long to long/short. In the middle of the image, the detected signal has zero chirp. This effect causes spectroscopic noise by appearing as a center wavelength shift in the detected spectra at isolated reflecting or scattering surfaces, regardless of the optical properties of the tissue being imaged. Since the reference path dispersion was varied by inserting and removing BK7 glass, the apparent position of the mirror in the OCT image also varied due to changes in the system’s zero delay. Cross-correlation was used after data acquisition to partially remove this effect.

A third significant source of spectroscopic noise is related to the bulk optical scattering properties of biological tissue. The overall scattering efficiency of tissue is higher for shorter wavelengths; therefore, a general red-shifting trend is observed in the detected spectra at increasing axial depths, since the shorter wavelengths do not penetrate as deeply into the tissue. This effect was visible in the spectroscopic images presented previously, where the center wavelength of the detected spectra was used as the spectroscopic metric [2]. Red-shifting of the spectra due to bulk scattering can degrade the ability of such systems to discern fine spectroscopic features of the tissue at deep axial positions, since the spectral shift due to bulk scattering can be larger than the shift due to spectroscopic features of interest. The scattering background can be removed with a variety of mathematical techniques [4,17] at the expense of increased computation time, but it would be advantageous to develop a spectroscopic analysis technique that is immune to the effects of bulk scattering by nature of the metric itself.

5. Spectral modulation as a spectroscopic OCT metric

After a local spectrum has been calculated for each pixel in the OCT image using an STFT, it is necessary to quantify some aspect of the spectra for display and evaluation. Previous work has used the center wavelength of the spectra as the spectroscopic metric [2,3]. It has also been shown that measuring spectral modulation can be used to extract information about the size of biological scattering particles [6–13].

When a single scattering sphere is illuminated by a coherent light source, the spectral modulation pattern on the backscattered light is well-defined by Mie theory and the exact size of the particle can be extracted by analyzing the spectrum. When multiple scattering spheres with a distribution of sizes, refractive indices, and number densities are illuminated simultaneously, the backscattered fields interfere coherently with one another in a stochastic process. An equivalent process occurs in intensity-based OCT imaging, where multiple scattering particles within the imaging volume defined by the beam diameter and coherence length create stochastic interference commonly referred to as speckle [18]. In spectroscopic OCT imaging, speckle is visible in both the intensity of the backscattered light and the modulation patterns of the local spectra. The spectral modulation present at each pixel in the image can therefore be considered as an outcome of a stochastic process, where the properties of the process are determined by the distribution of sizes and refractive indices of the cellular organelles contained within the imaging volume, as well as the number density of the organelles. By analyzing the statistical properties of the local spectra, information about the underlying distribution of scattering particles can therefore be generated.

One way to obtain information about the distribution of scattering particles at each point in the image is to examine the autocorrelation function r_XX[m] of the local spectra X_n[k], given by

Regions containing smaller particles produce less spectral modulation, while regions containing larger particles produce more modulation. The number density of the scattering particles also affects the modulation pattern. Regions with a higher particle density and a wider distribution of sizes produce spectra with more modulation compared to regions with low particle density and a narrower distribution of sizes. The autocorrelation of the local spectra take on distinct shapes as the spectral modulation pattern changes. Small amplitude, low frequency modulations corresponding to areas with mainly small particles [19] produce an r_XX[m] that falls off slowly around m=0, with few secondary peaks. Conversely, large amplitude, high frequency modulations corresponding to areas with mainly large particles [19] produce an r_XX[m] that falls off rapidly around m=0, with many secondary peaks. The bandwidth of the autocorrelation function can therefore be used to provide information about the distribution of scattering particle sizes at each point in the spectroscopic OCT image, representing the data as a single r_XX[m] bandwidth value that can be encoded into an HSL color map.

Using the autocorrelation function bandwidth as a spectroscopic metric provides an analysis technique that is insensitive to all sources of spectroscopic noise that appear as local Doppler shifts. Spectroscopic noise caused by nonuniform reference arm scanning, incident pulse chirp, and red shifting with increased tissue depth are all manifested as local Doppler shifts in the detected spectra. Since the bandwidth of the autocorrelation function does not depend on the absolute optical wavelengths that the spectral power is distributed over, it is insensitive to Doppler shifts. Therefore no additional system components are required to compensate for the motion of the reference arm, and image contrast is improved by rejection of incident pulse chirp and depth-dependant red shifting. One drawback to this approach is that quantitative information regarding optical absorption at specific wavelengths is not available.

To evaluate the ability of spectroscopic OCT to differentiate tissue types based on scattering particle size, a series of solutions containing polystyrene microspheres with diameters of 200 nm, 800 nm, 5 µm, and 20 µm, and refractive index of 1.59 were imaged and their optical spectra were calculated using a CZT-based STFT. The solutions were placed in plastic containers and covered with a glass coverslip. The CZT was set to span optical wavelengths between 600 nm and 1000 nm, using a number of points equal to the window length. For the 200 nm and 800 nm microsphere solutions, the full-width-half-maximum (FWHM) of the Hamming window was set to be slightly larger than the coherence length of the OCT system, giving a window length of ~400 points. This was rounded up to 512 points to decrease the algorithm execution time, resulting in a final window spanning 8.6 µm in water with a FWHM of 2.7 µm in water. For the 5 µm and 20 µm microsphere solutions, the FWHM of the window was adjusted to be slightly larger than the size of the microspheres to isolate spectra from single particles within the analysis window. Since the ability to resolve rapid spectral modulations decreases as the window size is decreased, the window sizes were increased slightly for each measurement and it was verified that no new high-frequency modulations became visible.

Within the imaging volume (5 µm×1.5 µm in water), the number densities of the 200 nm, 800 nm, 5 µm, and 20 µm solutions were 94, 1.5, 6×10^-3, and 9.4×10^-5 particles respectively. Accordingly, the 800 nm and 200 nm solutions are expected to exhibit spectral modulation profiles consistent with scattering from multiple particles within the imaging volume, while the 5 µm, and 20 µm solutions were expected to exhibit profiles consistent with isolated particle scattering. For the 5 µm and 20 µm solutions, the center of the window was placed in the center of an individual particle to obtain a representative spectrum. For the 200 nm and 800 nm solutions, the exact location of the center of the window was not critical since the particle density within the imaging volume was greater than unity.

Figure 4 shows representative spectra for a glass coverslip and the 20 µm, 5 µm, 800 nm, and 200 nm microsphere solutions. The spectra were obtained from ~100 µm below the coverslip, matching the focal point of the incident beam. Based on the number density of the microspheres, the incident beam is expected to interact with ~6000 particles in the 200 nm microsphere solution and ~100 particles in the 800 nm solution before propagating to ~100 µm in depth. Therefore for the 200 nm and 800 nm solutions, bulk scattering effects from microspheres above the imaging volume are present. For the 5 µm and 20 µm solutions, it is possible that the detected spectra are from single scattering, without the effects of bulk scattering. It is therefore possible that under higher density conditions with bulk scattering effects present, the spectra for the 5 µm and 20 µm solutions may be different than those presented here. However, since the main effect of bulk scattering is to produce attenuation of the incident beam with propagation depth, the spectral modulation pattern should not be significantly affected.

As expected, the 20 µm particles exhibit more modulation than the 5 µm particles, since each of the spectra in these cases are the results of isolated particle scattering. The degree of modulation of the spectra for the 200 nm and 20 µm solutions appear similar to one another, and also appear more modulated than the isolated particle scattering from 5 µm microspheres. This is likely due to the fact that the 200 nm solution contained 94 particles per OCT imaging volume, while the 20 µm solution contained less than one particle per imaging volume. It therefore appears that the spectrum resulting from ~100 of the 200 nm particles is approximately equivalent to the scattering spectrum of a single 20 µm particle, at least within the sensitivity limit of the current spectroscopic OCT system. Nevertheless, the calculated spectra for the coverslip, 5 µm, 200 nm, and 800 nm microspheres all contain significantly different amounts of spectral modulation.

 

Fig. 4. Detected spectra from a glass coverslip and regions containing 20 µm, 5 µm, 800 nm, and 200 nm microspheres. 20 µm and 5 µm microspheres induce spectral modulation consistent with isolated particle Mie scattering. 800 nm and 200 nm microspheres induce modulation consistent with scattering from multiple particles.

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This points out an inherent problem with spectroscopic metrics based on spectral modulation: in some cases they may be unable to distinguish a single large scatterer from many smaller scatterers within a single imaging volume. It is important to note that quantitative in vivo particle sizing techniques such as light scattering spectroscopy [6–13] may not display the same ambiguity, since these methods average over larger volumes and often use polarization- or angle-sensitive measurements combined with rigorous Mie theory modeling to extract accurate particle size information from backscattered spectra. For applications requiring quantitative point measurements of particle size, light scattering spectroscopy may be a more suitable method. The spectroscopic OCT technique that is the subject of this study, however, is capable of providing qualitative information about the distribution of particle sizes to enhance the contrast of an OCT image.

Figure 5 shows the autocorrelation functions of the optical spectra obtained from a glass coverslip and from solutions containing 20 µm, 5 µm, 800 nm, and 200 nm polystyrene microspheres. The spectrum of the coverslip exhibits the lowest degree of modulation, while the spectrum of the 800 nm microspheres exhibits the most modulation. The 5 µm microspheres fall in between, while the 200 nm and 20 µm microspheres appear very similar. It is evident that the shapes of the spectral autocorrelation functions change significantly depending on the degree of spectral modulation and therefore the scattering particle size. Figure 5 also illustrates that the autocorrelation functions of different sized particles can appear similar when the concentrations are not equal. The bandwidth of r_XX[m] varies significantly depending on the degree of spectral modulation present. The largest difference is seen in the region near m=0, where modulated spectra cause the autocorrelation function to fall off rapidly and non-modulated spectra fall off slowly. Therefore, by evaluating the bandwidth of r_XX[m], it is possible to obtain a measure of spectral modulation. The exact point at which the bandwidth is calculated can be adjusted, but should be near the peak of r_XX[m]. Experimentally, using the bandwidth at 90% of the peak was found to provide good spectroscopic contrast, as shown in Fig. 5. However, the choice of the convention for autocorrelation bandwidth represents an additional parameter which must be optimized for given analysis applications.

Finally, it is important to note that our results may not apply to the limit where scattering effects are extremely strong and deep structures are imaged. In this limit, multiple scattering events can dominate the contribution to the OCT signal instead of single scattering.

 

Fig. 5. Autocorrelation of the optical spectra for a glass coverslip and regions containing 20 µm, 5 µm, 800 nm, and 200 nm microspheres. Characteristic differences are observed in the bandwidth, shape, and number of peaks in the autocorrelation functions. These properties are related to the degree of spectral modulation caused by the target. Insert: The bandwidth at 90% of the peak can be used as one measure which differentiates particle sizes.

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6. Spectroscopic imaging of developmental biology specimens

The spectroscopic analysis technique was evaluated by in vivo imaging of a developing zebrafish embryo and a developing Xenopus Laevis (African frog) tadpole. In both cases a 256-point Hamming window was used, corresponding to a total length of 4.3 µm in tissue and a FWHM of 1.4 µm in tissue. The window position was incremented in steps of 60 points such that the axial pixel resolution of the intensity-based data (saturation and luminance) in the final images is 1.0 µm in tissue, slightly less than the coherence length of 1.5 µm. The autocorrelation bandwidth at 90% of the peak was calculated for each local spectrum and mapped into the hue value of a HSL color map. Saturation and luminance were obtained from the intensity of the software demodulated A-scans. Cross-correlation was used to remove motion artifacts from the images. No other signal processing was used, and no exogenous contrast agents were applied to the specimens. For comparison, a spectroscopic analysis was performed using center wavelength as the spectroscopic metric, mapping center wavelength into hue and mapping intensity of the demodulated data into saturation and luminance.

 

Fig. 7. Intensity-based OCT image of an in vivo developing zebrafish embryo.

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Fig. 8. In vivo spectroscopic OCT image of a developing zebrafish embryo using the center wavelength as the spectroscopic metric. No contrast enhancement between the embryo, membrane, and nutrients is observed. Spectroscopic noise from galvanometer motion and chirp of the incident pulses is present.

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Fig. 9. In vivo spectroscopic OCT image of a developing zebrafish embryo using the autocorrelation bandwidth of the optical spectra as the spectroscopic metric. Improved contrast between the embryo, membrane, and nutrients is obtained. Spectroscopic noise from nonuniform reference arm galvanometer motion and chirp of the incident pulses is not present.

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Figures 7–9 show OCT images of a developing zebrafish embryo using standard intensity-based OCT imaging, spectroscopic imaging using center wavelength as the spectroscopic metric, and spectroscopic imaging using autocorrelation bandwidth as the metric. The standard intensity-based image is shown in Fig. 7. The center wavelength analysis in Fig. 8 is not corrected for reference arm motion nonuniformity, and therefore shows alternating red and green horizontal bars running through the image, which are the result of changes in the galvanometer velocity as the A-scans are acquired. The suspended nutrient concentrations in the nutrient sac, as well as the embryo membrane and Petri dish, all show the effects of incident pulse chirp. The embryo, embryonic membrane, and nutrients are not spectroscopically differentiated. Conversely, the autocorrelation bandwidth analysis in Fig. 9 shows good contrast between the various sections of the specimen. Galvanometer noise and chirp noise are not present. In this image, red areas indicate a narrower 90% autocorrelation bandwidth, and therefore indicate areas of higher spectral modulation. Blue areas indicate a broader bandwidth and lower modulation. Compared to the intensity-based OCT image and the center wavelength analysis, the spectroscopic analysis technique using the autocorrelation function bandwidth enhances tissue contrast and is insensitive to spectroscopic noise sources.

 

Fig. 10. In vivo OCT images of a developing Xenopus Laevis (African frog) tadpole, using standard intensity-based imaging (A), spectropscopic imaging using center wavelength as the metric (B), and spectroscopic imaging using the autocorrelation function of the optical spectra as the metric (C). Galvanometer noise and red-shifting are present in (B), and no significant contrast enhancement is obtained. No spectroscopic noise is present in (C), and enhanced contrast between the different tissue types of the specimen is achieved.

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Figure 10 shows images of a developing Xenopus Laevis (African frog) tadpole using standard intensity-based OCT imaging, spectroscopic imaging using the center wavelength as the spectroscopic metric, and spectroscopic imaging using autocorrelation bandwidth as the metric. The standard intensity-based image is shown in Fig. 10(a). Note that in this specimen, as with the zebrafish embryo, the center wavelength analysis shown in Fig. 10(b) does not provide any significant contrast enhancement of the various tissue types within the sample when compared to the intensity image. Noise from nonuniform galvanometer reference arm scanning is again visible as alternating red and blue horizontal lines, and red-shifting is observed in deeper regions of the tadpole. Figure 10c shows the image using the autocorrelation bandwidth as the spectroscopic metric. No spectroscopic noise is visible, and good contrast enhancement is obtained between the various structures within the tadpole. The outer membrane and tail cartilage appear yellow, while the region inside the membrane appears blue. Structures inside the developing head appear yellow and red, while some smaller structures contain a blue (highly modulated) center. Overall, the autocorrelation function bandwidth appears to be a good metric that is insensitive to spectroscopic noise and capable of providing good contrast enhancement.

7. Conclusions

In summary, this manuscript presented new methods for performing spectroscopic OCT. The use of the chirp z transform (CZT) to implement a short time Fourier transform (STFT) was shown to provide a more efficient means for the analysis of interferometric A-scan fringe data by concentrating all of the points in the transform within a frequency region of interest. Spectroscopic OCT based on a statistical analysis of spectral modulation caused by variations in scattering particles sizes was shown to have several advantages over previous methods based on an analysis of center wavelength. This technique constructs the autocorrelation function of the detected optical spectrum at each point in the image as a statistical measure of the spectral modulation. The bandwidth of the autocorrelation function is used as a metric for image display and the autocorrelation bandwidth is represented as the hue of a HSL color map. Saturation and luminance are obtained from the intensity of the demodulated A-scans, preserving the spatial resolution of the structural information and decoupling it from the spatial resolution of the spectroscopic information. This technique has the advantage that it is insensitive to many sources of spectroscopic noise.

Studies of model systems using varying diameter microspheres show that the spectral modulation and the bandwidth of the spectral autocorrelation function are related to both particle size as well as the number of particles present in the volume of imaging defined by the coherence length and focal spot size. In addition, imaging studies of development biology specimens in vivo show that this method enhances differentiation of different tissue structures and eliminates the effects of major spectroscopic noise sources, without the need for exogenous contrast agents. These studies point to the importance of considering statistical effects from multiple particles to account for scattering spectra in addition to isolated particle scattering effects. These effects of scattering from multiple particles can make direct measurements of particle size challenging, but with appropriate spectroscopic metrics it is possible to enhance contrast for different tissue types. Spectroscopic OCT can provide improved imaging compared to standard OCT techniques based on intensity alone.