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Abstract
We present a holographic tomography technique in which the projections are acquired using both wavelength and illumination scanning in the near-infrared region. We show how to process the acquired data to obtain correct values of three-dimensional refractive index distributions in both single-wavelength and multi-wavelength data acquisition schemes and how to properly account for the dispersion of the sample. We perform numerical and experimental comparisons of different illumination scenarios to determine the most efficient measurement protocol. We show that the multi-wavelength protocol is advantageous in terms of signal-to-noise ratio and contrast-to-noise ratio over single-wavelength protocols, even for the same number of projections used for reconstructions. Finally, we show that this approach is suitable for providing high-quality refractive index distributions of relatively thick colon cancer samples.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical diffraction tomography (ODT) with holographic projections, also known as holographic tomography (HT), is an interferometric technique that enables reconstruction of sample’s three-dimensional (3D) refractive index (RI) distribution by measuring scattered object fields at various angles [1]. Among its many advantages, HT does not require the use of labeling agents or dyes since the measured RI is used as an imaging contrast [2]. This eliminates the complicated sample preparation process. Moreover, the reconstructed RI is a quantitative parameter which can be converted into cellular dry mass - the important biophysical parameter [3,4].
Most transmission-mode ODT systems record multiple complex amplitudes of optical fields diffracted by the measured object under varying illumination angles, using monochromatic illumination. This is usually realized either by rotating the sample while the illumination beam is fixed [5] or by rotating the illumination [6]. Regardless of the illumination method chosen, the captured optical fields should fill the Fourier space (K-space) of the tomographic reconstruction to the extent sufficient to reconstruct the RI distribution of the measured sample. However in the case of the illumination rotation method, which is most popular in biomedical applications, the reconstruction is associated with strong missing-cone artifacts [7]. For a fixed maximum illumination angle in the system, the quality of the reconstructed RI map of the transmission-mode ODT with monochromatic light depends on the optimal K-space filling, which is directly connected with the utilized illumination pattern and the number of projections. Taddese et al. investigated different illumination patterns in these regards [8].
Another way to improve the imaging quality is to use multi-wavelength illumination [9–14]. On one hand this method can be used to enhance signal-to-noise ratio (SNR) through averaging multiple measurements of the same sample in the K-space. On the other hand, it can increase the coverage of the K-space leading to higher resolution of tomographic reconstructions. Multiple-wavelength tomography can be performed by capturing several projections with scanned wavelength for each illumination direction. Despite the application potential, merely a few applications of multi-wavelength illumination in ODT have been reported yet to improve the imaging quality or limit the number of illumination directions. Hosseini et al. developed an ODT system that provides 3D RI map of a sample by scanning the wavelength of three illumination beams [15], however the illumination directions were captured simultaneously, which degraded the reconstruction quality. Moreover, the dispersion analysis of the acquired results has not been presented which may be important for certain biological samples, especially in the visible spectrum. On the contrary, Zuo et al. proposed a lensless quantitative phase microscopy and diffraction tomography based on a compact on-chip platform with programmable color LED matrix [16]. In this case partially coherent multi-angle LED illumination at different wavelengths effectively suppress the speckle noise and distortions caused by parasitic reflections in the optical setup. However, the number of generated wavelengths is limited by the utilized light source to three ones (each LED of the LED matrix can provide approximately spatially coherent quasi-monochromatic illuminations with narrow bandwidth centered at: 623nm, 522nm and 467nm). The microscopic technique referred to as hyperspectral ODT [17], in turn, was used for spectroscopic applications rather than improving the imaging quality using accessible spectrum. Next, multi-wavelength multi-angle tomographic microscope presented in Ref. [18] operates in a reflection mode and captures only high frequency components of the object’s scattering potential, thus the reconstruction of the RI distribution is not possible [19]. Furthermore, it should be emphasized that all of the aforementioned tomographic methods use visible light for illumination.
In this paper, we present wavelength and illumination scanning holographic tomography (WIS-HT). The presented imaging system differs from state-of the-art HT systems by the use of a broadband, tunable illumination source operating in the near-infrared (NIR) region and allows for designing various strategies of scanning the illumination and wavelengths for biological applications, where low scattering [20] and low photodamage [21] are key properties. In particular, we show the NIR illumination penetrates deep in the scattering biological medium allowing for imaging relatively thick colon cancer sample. Furthermore, we show that for the same number of acquired holograms the use of multi-wavelength illumination scenarios allow for increased contrast-to-noise ratio as compared to single-wavelength illumination scenarios. Additionally, the comprehensive dispersion analysis is provided for WIS-HT.
In Section 2. we provide a description of the measurement system, measurement protocols used in the experiments and measurement samples. In Section 3. the methods of data analysis are characterised. Next, in Section 4. different measurement protocols are compared to validate RI imaging quality: (Section 4.1) presents simulated results for PMMA microbead and cell microphantom while in Section 4.2 the experimental results for PMMA microbead, cell microphantom and colon cancer sample as a representation of the biological sample, are shown.
2. Methods
2.1 Experimental setup
The measurement system used in this work is depicted in Fig. 1. It is based on a Mach-Zehnder interferometer (MZI). The light source used in this work (Superlum Broadsweeper BS-840-2-HP) provides wavelength range $\lambda$=800-870nm (controllable with increments of $\Delta \lambda$=0.05nm) with nominal linewidth L=0.12nm (which translates to coherence length $l_{c}$=1.7mm) and 20mW maximum power. In the object beam there is a galvanometer scanner imaged onto the sample plane with a first 4f microscope system (tube lens and microscope objective) at transverse magnification M=-83.3. The sample is then imaged onto the camera plane by a second 4f microscope system (M=-72.7), represented with MO2 and TL in Fig. 1. As a result, the optical path difference (OPD) in the two branches of the interferometer is estimated as $L_{OPD}$=57mm, which exceeds the coherence length of the source. For this reason a retro-reflective module was used to compensate the OPD (see the OPD adjustment module in Fig. 1).
Fig. 1. Measurement system used in this work. GM: galvo system Thorlabs GVS212/M, L2: lens, effective focal length EFL=150mm, MO1 and MO2: 40x NA 1.3 oil immersion microscope objectives, SPL: sample plane, TL: lens, EFL=300mm, BS1: (30T:70R) beam splitter, OI: Optical Isolator, SS: Superlum Broadsweeper BS840-2-HP, OPD: optical path difference adjustment module.
2.2 Measurement protocols
The measurement protocols were selected in order to compare the quality of 3D RI reconstruction (see Section 3.1) of the wavelength and illumination scanning holographic tomography and single wavelength illumination scanning HT. The measurement protocols are listed in Table 1. Protocol $\boldsymbol{0}^{1\lambda }_{a}$ is the most common scenario that uses annular scanning pattern for a single wavelength of illumination ($\lambda$=835nm) and 181 illumination directions ($\sim \!\!45^{\circ }$ polar angle in the sample plane, close to the NA limit of the experimental setup), including one incident projection with the normal illumination. Protocols $\boldsymbol{A}^{1\lambda }_{u}$ and $\boldsymbol{B}^{N\lambda }_{a}$ have the same total number of projections, however $\boldsymbol{A}^{1\lambda }_{u}$ utilizes UDHS (3D uniform distribution on a hemisphere [8]) scanning pattern with 1 illumination wavelength ($\lambda$=835nm) whereas $\boldsymbol{B}^{N\lambda }_{a}$ uses multi-wavelength annular scanning with 181 projections for each wavelength. Each multi-wavelength measurement or simulation was performed for the entire available spectrum of the swept-source laser (70 nm) and wavelength step of 1nm, resulting in 71 samples per each illumination direction (see Table 1).
Table 1. Measurement protocols and scanning patternsa
In this work we compare the above protocols to validate RI imaging quality. First, protocols $\boldsymbol{0}^{1\lambda }_{a}$ and $\boldsymbol{B}^{N\lambda }_{a}$ are compared in terms of the PMMA bead RI measurement accuracy. Then, protocols $\boldsymbol{0}^{1\lambda }_{a}$, $\boldsymbol{A}^{1\lambda }_{u}$ and $\boldsymbol{B}^{N\lambda }_{a}$ are compared for cell microphantom (simulation and experiment) and colon cancer sample (experiment) to investigate the improvement in quality by providing the quality metrics introduced in Section 3.1.
Figure 2 shows 2D cross-sections ($k_{x}\!-\!k_{z}$) through optical transfer functions (OTFs) that correspond to measurement protocols described above. As shown in Fig. 2, the OTF for protocol $\boldsymbol{A}^{1\lambda }_{u}$ covers larger frequency band in Fourier space than protocols $\boldsymbol{0}^{1\lambda }_{a}$ and $\boldsymbol{B}^{N\lambda }_{a}$ (annular scanning patterns). In order to quantify those differences, we calculated K-space filling factor ($FF_{Kspace}$) for each OTF presented in Fig. 2 and summarized the results in the last column of Table 1. We define K-space filling factor, based on the one reported in [8], as:
where $V_{OTF}$ represents the number of voxels contained in the OTF, while $V_{Kspace}$ represents the number of voxels of the smallest K-space that encompasses any of considered OTFs. The obtained $FF_{Kspace}$ values suggest that protocol $\boldsymbol{A}^{1\lambda }_{u}$ should outperform protocols $\boldsymbol{0}^{1\lambda }_{a}$ and $\boldsymbol{B}^{N\lambda }_{a}$ in terms of RI imaging quality. In Section 4. we show the results that quantify the differences between those protocols in this regard.Fig. 2. 2D cross-sectional images ($k_{x}\!-\!k_{z}$) of the OTFs for protocols from Table 1: (a) protocol $\boldsymbol{0}^{1\lambda }_{a}$, (b) protocol $\boldsymbol{B}^{N\lambda }_{a}$ and (c) protocol $\boldsymbol{A}^{1\lambda }_{u}$. The corresponding scanning patterns are visualized in the square boxes (the number of points was limited to 181 in image (c)).
2.3 Numerical samples
Two numerical samples were used in simulations: cell microphantom and microbead. In the simulations, object projections were generated with Fourier Diffraction Theorem [22] by computing object’s 3D spectrum, extracting part of the spectrum that corresponds to specific wavelength and illumination direction and inverse Fourier transforming the extracted data. In order to simulate real measurement conditions, Gaussian noise was added to the projection data of both cell microphantom and PMMA microbead (SNR=25dB that corresponds to the noise level measured in the experiments). Both numerical samples used in simulations were represented by 3D arrays of discretized RI distributions and size 222$\times$222$\times$222 voxels with voxel size $dx\!=dy\!=\!dz\!=\!0.288\mu m$; the size of simulated projections (amplitude and phase) remained the same: 222$\times$222 pixels with pixel size $dx\!=\!dy\!=\!0.288\mu m$. For each simulation wavelength, a modified instance of 3D numerical sample representation was generated according to material dispersion formula ($\lambda$ expressed in micrometers):
(i) PMMA material [23] (microbead):
(ii) IP-DIP polymer [24] (cell microphantom):
where: $A\!=\!1.5273$, $B\!=\!6.5456\!\times \!10^{-3}$, $C\!=\!2.5345\!\times \!10^{-4}$, $d_{corr}\!=\!-0.006026805$; $d_{corr}$ is a correction factor for RI offset of the polymer that arises due to the different fabrication parameters (under assumption that the dispersion of the material does not change at various degrees of polymerization);
(iii) Immersol 518F oil $n(\lambda )$ expressed by Eq. (3) for $A\!=\!1.498371158$, $B\!=\!5856.100359$, $C\!=\!0.1299$ and $d_{corr}\!=\!0$ according to the manufacturer’s specification.
2.4 Experimental samples
Two types of samples were tested experimentally: (1) PMMA (polymethyl methacrylate) microbead and cell phantom which were physical twins of the numerical samples from Section 2.3 and (2) an example of a complex biological sample.
2.4.1 PMMA bead and cell microphantom
The PMMA bead (23.5$\pm$0.36 $\mu$m diameter, microParticles GmbH) and the cell microphantom made of IP-DIP polymer (first described in [25]) have been immersed in Immersol 518F (Carl Zeiss AG) and sandwiched between two #1 coverslips (0.13-0.16mm) separated by 80 $\mu$m spacer. Selected object immersion oil ensures that the RI contrast within the sample is comparable to the biological specimens in their medium. Both samples have been introduced to the system in the sample chamber located inbetween the microscope objectives (SPL in Fig. 1) with the appropriate objective immersion oil (also Immersol 518F).
2.4.2 Colon cancer specimen
Histopathologic sections of 15$\mu$m thickness were cut from formalin-fixed paraffin-embedded tissue block of human colon cancer using a RM2265 rotary microtome (Leica Biosystems, Nussloch, Germany) and applied on #1 coverslips 24mm $\times$ 60mm (Menzel-Gläser, Braunschweig, Germany). The samples were incubated at $56^{\circ }$C for 30 minutes, dewaxed in xylene for 6 hours, rehydrated in ethanol solutions of descending concentrations (99.8%, 80%, 50%) and distilled water, for 15 minutes each. The medium for mounting the specimens constituted a solution of PBS pH 7.4 with glycerol (1:1 v/v).
3. Data analysis
In order to examine the potential of the method, 3D RI reconstructions of the measured samples (numerical and experimental) were computed by calculating the inverse Fourier transform of the spectrum filled with captured projections (direct inversion method; DI) [6] or using a Gerchberg-Papoulis (GP) iterative algorithm [6,26], which significantly minimizes reconstruction artifacts due to the missing cone problem [27]. As an input to the solvers (reconstruction software) [28], the experimental projections were calculated through Fourier-processing of off-axis holograms acquired with the optical system. In Section 3.1 we introduce metrics that are used to determine the enhancement in RI imaging due to the applied measurement protocol. Next, in Section 3.2 we explain the way of processing 3D reconstruction data in order to calculate PMMA bead RI for single-wavelength and multi-wavelength measurement protocols.
3.1 Imaging quality
Contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR) are the parameters used to determine the quality of image and frequently applied e.g. in magnetic resonance imaging (MRI) [29–31]. We adopted these metrics to study and compare the quality of ODT reconstruction based on different measurement scenarios. We define CNR as:
where $C$ is an RI image contrast measured as a difference between mean values ($S_{1}$ and $S_{2}$) of two regions sampled in the object part of the RI image (ROI 1 and ROI 2, see for example Fig. 5), while $\sigma _{noise}$ is a standard deviation of noise sampled from the object-free background (noise ROI, see for example Fig. 5) assumed to be the immersion part. We found that noise distribution for the obtained RI images can be assumed Gaussian, thus no other noise sampling is required [29]. Moreover, the dynamic range in the object area is also taken into account since ROI 1 and ROI 2 are sampled from two object’s regions of extreme mean RI values. With such a definition of CNR, we calculate SNR simply as: were $S_{1}$ and $\sigma _{noise}$ are the quantities used to calculate CNR. SNR values are given in decibels.We clearly emphasize here that our intention was to investigate some aspects of the quality of RI imaging, mostly manifested by improvement in SNR due to wavelength diversity. This approach does not take into account the enhancement in resolution that strictly results from the experimental or simulated OTFs.
3.2 Refractive index reconstruction
The general scheme of the 3D RI reconstruction algorithm is based on the DI method (Fig. 3(a)). In brief, each of the acquired 2D holograms is filtered to remove the DC component, the complex conjugate of the object spectrum, and the carrier frequency. Next, the resulting complex valued 2D hologram (sinogram) is 2D Fourier transformed after applying the Rytov approximation, and placed in the 3D K-space [6]. The K-space filled with all the acquired data is 3D inverse Fourier transformed resulting in a 3D scattering potential map. The RI distribution $n(\lambda _{rec})$ for a single wavelength $\lambda _{rec}$ is recalculated from the scattering potential using equation from Fig. 3(a) with values of immersion medium RI, $n_{imm.}(\lambda _{rec})$, and axial component of wavevector, $k(\lambda _{rec})$, calculated for this wavelength. This general approach can be directly applied to data acquired using protocol $\boldsymbol{0}^{1\lambda }_{a}$ or $\boldsymbol{A}^{1\lambda }_{u}$. Since we also scan the wavelengths, the procedure is simply repeated for $N$ single-wavelength data. This leads to $N$ reconstructed 3D RI distributions, as shown in Fig. 3(b).
Fig. 3. (a) Refractive index reconstruction using the DI method. $n^{\scriptscriptstyle 3D}_{\scriptscriptstyle distr.}$ - 3D RI distribution, $n_{imm.}(\lambda _{rec})$ - RI of immersion medium for $\lambda _{rec}$, $IFT\{K\!-\!space\}$ - scattering potential (inverse Fourier transform of the K-space representation), $\lambda _{rec}$ - wavelength used in the reconstruction, $k(\lambda _{rec})$ - length of wavevector ($Z$-component) for wavelength $\lambda _{rec}$. (b) DI method applied to data acquired in protocol $\boldsymbol{0}^{1\lambda }_{a}$. The $n^{\scriptscriptstyle 3D}_{\scriptscriptstyle distr.}$ for $N$ wavelengths is obtained by applying the DI method separately to each single-wavelength dataset. (c) DI method applied to data acquired in protocol $\boldsymbol{B}^{N\lambda }_{a}$. The $n^{\scriptscriptstyle 3D}_{\scriptscriptstyle distr.}$ for $N$ wavelengths is obtained by applying the DI method to a single K-space filled with data from all the wavelengths but reconstructed $N$ times for different $\lambda _{rec}$.
In case of data acquired using protocol $\boldsymbol{B}^{N\lambda }_{a}$, shown in Fig. 3(c), we fill a single K-space with all the projections coming from all the angles and all the wavelengths. Then, a single scattering potential ($\!IFT\{K\!-\!space\}$) is obtained. According to equation shown in Fig. 3(a), a single wavelength $\lambda _{rec}$ should be used to calculate the 3D RI distribution.
This $\lambda _{rec}$ value cannot be chosen arbitrarily to obtain the correct RI. In Fig. 7 we show the procedure for determining $\lambda _{rec}$ for which the reconstructed RI falls within the standard deviation of RI from single-wavelength measurement ($\lambda ^{rec}_{\scriptscriptstyle ideal}$ in Fig. 3(c)). In this procedure we compare RI distributions (mean RI values in Fig. 7) obtained using single-wavelength and multi-wavelength approaches for $N$ consecutive $\lambda _{rec}$. The results of this analysis are presented in Section 4.2.1 and allowed us to verify the choice of $\lambda _{rec}$ used in PMMA RI calculations for protocol $\boldsymbol{B}^{N\lambda }_{a}$. We show in the following Sections that for a properly selected wavelength, $\lambda ^{rec}_{\scriptscriptstyle ideal}$, the approach from Fig. 3(c) (protocol $\boldsymbol{B}^{N\lambda }_{a}$) is advantageous compared to Fig. 3(a) (protocols $\boldsymbol{0}^{1\lambda }_{a}$ and $\boldsymbol{A}^{1\lambda }_{u}$) in terms of CNR and SNR, even for the same number of projections.
4. Results
In this Section different measurement protocols are compared to investigate RI imaging quality. In Section 4.1 we present simulated results for PMMA microbead and cell microphantom while in Section 4.2, the experimental results for PMMA microbead, cell microphantom and colon cancer sample are shown.
4.1 Simulated results
Numerical analysis was performed for simulated sinograms obtained for PMMA bead model (simple object), with the aim to verify improved imaging quality and for numerical cell microphantom (complex object) in order to emphasize this improvement quantitatively.
First, we compare the 3D RI reconstructions obtained with GP iterative reconstruction method of simulated PMMA bead model for protocol $\boldsymbol{0}^{1\lambda }_{a}$ and $\boldsymbol{B}^{N\lambda }_{a}$ with $\lambda$=835nm and noise added to projection data. The results are shown in Fig. 4, in which the improvement in quality of reconstructed RI maps can be observed for protocol $\boldsymbol{B}^{N\lambda }_{a}$ (Fig. 4(c,f)) over protocol $\boldsymbol{0}^{1\lambda }_{a}$ (Fig. 4(b,e)), expressed by suppressed noise.
Fig. 4. Simulation of RI distribution for PMMA bead model (noise added to projection data) reconstructed using GP method with $\lambda$=835nm. (a,d) Ground-truth RI distribution. RI reconstructed from data obtained with (b,e) protocol $\boldsymbol{0}^{1\lambda }_{a}$ and (c,f) protocol $\boldsymbol{B}^{N\lambda }_{a}$. Images (a-c) show xy cross-sections and (d-f) xz cross-sections.
Fig. 5. Tomographic reconstructions of the numerical cell microphantom (a,e). RI distributions (DI method) presented as a cross-sectional images obtained for: (b,f) protocol $\boldsymbol{0}^{1\lambda }_{a}$, (c,g) protocol $\boldsymbol{A}^{1\lambda }_{u}$ and (d,h) protocol $\boldsymbol{B}^{N\lambda }_{a}$. The dashed line in (c) indicates how the plots (i-j) where obtained: blue lines in both plots correspond to image (b), while red lines to images (c,d), respectively. The zoomed samples of images (b-d) are depicted in figures (k-m) where green and blue frames in image (m) indicate the ROIs selected from images (b-d) and used to calculate quality parameters; noise was sampled from the same images in the region marked by an orange frame in (d).
The second series of numerical analysis was performed for the cell microphantom numerical model (Section 2.3) in the context of RI imaging quality; the results are shown in Fig. 5. The analysis introduced here uses the metrics described in Section 3. The DI method was used in reconstructions to emphasize the influence of the applied illumination scenario on RI imaging quality, as shown in Fig. 5 and Table 2. One can observe a noticeably lower noise level for protocol $\boldsymbol{B}^{N\lambda }_{a}$ (Fig. 5(m) and red line in Fig. 5(j)) when compared with protocols: $\boldsymbol{A}^{1\lambda }_{u}$ (Fig. 5(l); red line in Fig. 5(i)) and $\boldsymbol{0}^{1\lambda }_{a}$ (Fig. 5(k); blue line in Fig. 5(i,j)). This improvement is presented quantitatively in Table 2 and also expressed in SNR and CNR but with no significant differences in image contrast C.
Table 2. Parameters used to assess the quality of the reconstructed RI images depicted in Fig. 5(b-d): image contrast C, contrast-to-noise ratio (CNR) and SNR (decibel scale). The standard deviation of sampled noise, $\sigma _{noise}$, is also provided in the last column
4.2 Experimental results
In this section we provide the analysis performed for experimental results, similar to that presented for simulations in Section 4.1. First, we analyze the results of PMMA microbead measurements (simple object) to verify the accuracy of RI reconstruction and the improvement in RI imaging quality. Next, we analyze experimental results obtained for cell microphantom and colon cancer specimen (complex objects) in order to quantify the improvement in RI imaging quality in practical setting. Furthermore, for colon cancer sample, we provide a biological description of the selected structures and processes visible in the RI images.
4.2.1 PMMA microbead and cell microphantom
Experimental results obtained for PMMA bead sample are presented in Fig. 6. The xy cross-sections through 3D RI reconstructions calculated with $\lambda$=835nm for measurement protocols (Table 1): $\boldsymbol{0}^{1\lambda }_{a}$ and $\boldsymbol{B}^{N\lambda }_{a}$ are shown in Fig. 6(a,b), respectively. The corresponding xz cross-sections are revealed in Fig. 6(c,d). The improved image quality is evident in Fig. 6(b,d) (protocol $\boldsymbol{B}^{N\lambda }_{a}$) when compared to protocol $\boldsymbol{0}^{1\lambda }_{a}$ (Fig. 6(a,c)), expressed by suppressed noise as with the corresponding simulated results from Fig. 4. This improvement is also visible in RI profiles shown in Fig. 6(e,f).
Fig. 6. Experimentally obtained RI distributions for PMMA bead reconstructed with $\lambda$=835nm (GP method) using (a,c) protocol $\boldsymbol{0}^{1\lambda }_{a}$ and (b,d) protocol $\boldsymbol{B}^{N\lambda }_{a}$. Images (a,b) show xy cross-sections while (c,d) the corresponding xz cross-sections. RI profiles (e,f) correspond to images (a,b): the blue line in both plots correspond to (a), as indicated by a dashed white line for profile (e), while red lines relate to image (b).
Fig. 7. Dispersion analysis of experimentally obtained PMMA bead RI performed as described in Section 3.2, Fig. 3. Ground-truth RI distribution calculated using Eq. (2) is plotted in black color. Mean RI values of the PMMA bead calculated from protocols $\boldsymbol{0}^{1\lambda }_{a}$ and $\boldsymbol{B}^{N\lambda }_{a}$ as a function of wavelength are plotted in blue (Fig. 3(b), for $N$=9) and red (Fig. 3(c), $N$=9), respectively.
Furthermore, we utilized the procedure described in Section 3.2 to perform a dispersion analysis for PMMA microbead to justify the efficacy of the RI reconstruction for protocol $\boldsymbol{0}^{1\lambda }_{a}$ (Fig. 3(b), for $N$=9) and protocol $\boldsymbol{B}^{N\lambda }_{a}$ (Fig. 3(c), $N$=9). We used PMMA microbead for the calculations of mean RI because of its simple structure (Section 2.4.1). Each RI value was calculated as a mean of voxel values encompassed by the mask defined as a sphere of diameter less than microbead diameter (0.64 times bead diameter) and center related to mass center in 3D RI data. Additionally, in case of experiments, bead diameter was calculated from xy cross-section of the corresponding 3D RI distribution by finding the edges of the bead.
The results of wavelength-dependent RI (material dispersion) are plotted in Fig. 7, in which error bars represent standard deviations relative to mean RI values (points in the plot). PMMA dispersion (protocol $\boldsymbol{0}^{1\lambda }_{a}$) for nine wavelengths of illumination (800-870nm range with 10nm step, including $\lambda _0$=835nm) is plotted in blue, while PMMA dispersion calculated using Eq. (2) (Section 2.3) is plotted in black color (ground-truth RI distribution). In the same plot, mean RI values calculated from protocol $\boldsymbol{B}^{N\lambda }_{a}$ with different wavelength $\lambda _{rec}$ used in RI computations, are plotted in red color. The reconstructed PMMA RI shown in Fig. 6(b,d) (protocol $\boldsymbol{B}^{N\lambda }_{a}$) was calculated with $\lambda _{rec}$=835nm, for which the dispersion curves (blue and red in Fig. 7) cross. This $\lambda _{rec}$ value is further used in all 3D RI reconstructions presented in this work. The results of calculation of PMMA bead mean RI and diameter, for $\lambda$=835nm, were also collected in Table 3.
Table 3. PMMA bead mean RI and diameter values. Mean RI values obtained with protocols $\boldsymbol{0}^{1\lambda }_{a}$ and $\boldsymbol{B}^{N\lambda }_{a}$ correspond to blue and red points in Fig. 7 for $\lambda$=835nm, respectively
One can see in Fig. 7 and Table 3 that wavelength-dependent mean RI values obtained for protocol $\boldsymbol{0}^{1\lambda }_{a}$ agree with those calculated using Eq. (3) (black color in Fig. 7, e.g. $n_{P\!M\!M\!A}(\lambda \!=\!835nm)=1.4837$). This comparison proves that we are able to reproduce $n(\lambda )$ of the measured material with high accuracy. It is also visible (Fig. 7, Table 3) that standard deviations for protocol $\boldsymbol{B}^{N\lambda }_{a}$ (red color) are noticeably lower than in the case of protocol $\boldsymbol{0}^{1\lambda }_{a}$ (blue color). This is due to the noise suppression in multi-wavelength measurement which results in improved RI reconstruction quality. We also measured a diameter of PMMA bead for protocols $\boldsymbol{0}^{1\lambda }_{a}$ and $\boldsymbol{B}^{N\lambda }_{a}$. The obtained values for each protocol (Table 3) were calculated as an average of four different measurements and agree with the value provided by the manufacturer (Section 2.4.1).
The next part of experimental results under our analysis was obtained for the cell microphantom sample described in Section 2.4.1. Here, we analyze the improvement in quality in the same way as with the simulated results presented in Fig. 5 and Table 2 for the numerical cell microphantom. Experimental results are depicted in Fig. 8. The cross-sections of the 3D RI reconstructions from Fig. 8(a-k) correspond to that presented in Fig. 5(b-d, f-m) for simulations, respectively. The same quality metrics were calculated and collected in both Table 4 (experiments) and Table 2 (simulations). One can note again, that there is a noticeably lower noise level for protocol $\boldsymbol{B}^{N\lambda }_{a}$ over both $\boldsymbol{A}^{1\lambda }_{u}$ and $\boldsymbol{0}^{1\lambda }_{a}$ and significant difference between $\boldsymbol{0}^{1\lambda }_{a}$ and $\boldsymbol{A}^{1\lambda }_{u}$, evident qualitatively when the images from Fig. 8(i-k) are compared. This improvement is also visible in RI profiles from Fig. 8(g,h). The differences in imaging quality between the considered protocols are also presented quantitatively in Table 4, expressed in $\sigma _{noise}$ (noise level), CNR and SNR parameters. Moreover, as it was shown in Table 2 (Section 4.1) for simulated cell microphantom, the differences in image contrast, C, are not significant, therefore we believe that the experimental differences are measurement-depended. Additional simulations (not shown) proved that correct RI with such SNR and CNR improvement is visible in the multi-wavelength approach for wavelength ranges ($\Delta \lambda$) at least up to 210nm. Besides, for high wavelength ranges care should be taken to include dispersion introduced by the imaging optics, however, in our setup with $\Delta \lambda$=70nm it did not impact the results.
Fig. 8. Comparison of experimental results obtained for the cell microphantom corresponding to that shown in Fig. 5 (simulations). The RI reconstructions were obtained using measurement protocols: (a,d) $\boldsymbol{0}^{1\lambda }_{a}$, (b,e) $\boldsymbol{A}^{1\lambda }_{u}$ and (c,f) $\boldsymbol{B}^{N\lambda }_{a}$. A dashed line in image (b) depicts how the plots (g-h) where obtained: blue lines in both plots correspond to image (a), while red lines in (g,h) correspond to images (b,c), respectively. The zoomed samples of images (a,b,c) are shown in figures (i,j,k); the green and blue frames in (k) indicate the ROIs selected from images (a-c) to calculate quality parameters.
Table 4. Parameters used to assess the quality of the reconstructed RI images depicted in Fig. 8(a-c)
4.2.2 Biological sample
In this Section we analyze the experimental results obtained for the colon cancer specimen described in Section 2.4.2. In particular, the two regions of the same specimen were measured and the obtained 3D RI reconstructions were visualised as a cross-sectional images and plots in Fig. 9 and Fig. 10 (region 1) and in Fig. 11 (region 2). We conducted a comprehensive analysis of the obtained results by calculating the quality metrics for protocols $\boldsymbol{0}^{1\lambda }_{a}$, $\boldsymbol{A}^{1\lambda }_{u}$ and $\boldsymbol{B}^{N\lambda }_{a}$ (Table 5) and providing the biological description, from the pathological point of view, of the structures and processes apparent in the RI images shown in Fig. 10 (region 1) and Fig. 11 (region 2) and reconstructed using GP method with protocol $\boldsymbol{B}^{N\lambda }_{a}$.
Fig. 9. Experimental results obtained for the colon cancer sample (region 1), presented as a xy (a-c) and xz (d-f) cross-sectional images of the 3D RI reconstructions computed using DI method and measurement protocols: (a,d) $\boldsymbol{0}^{1\lambda }_{a}$, (b,e) $\boldsymbol{A}^{1\lambda }_{u}$ and (c,f) $\boldsymbol{B}^{N\lambda }_{a}$. A dashed white line in image (d) indicates depth in which the (a-c) xy cross-sections were sampled, while a dashed line in (a) indicates how the plots (g-h) where obtained: blue lines in plots (g,h) correspond to image (a), while red lines correspond to images (b,c), respectively. Images (i-k) were obtained in the same manner as those presented in Fig. 8(i-k), for cell microphantom.
Fig. 10. The same experimental comparison as shown in Fig. 9, except the 3D RI distributions were reconstructed by means of GP iterative algorithm. In image (c), sections through the crypts within the colonic mucosa are marked with red and yellow arrows while the blue arrow indicates the area of the desmoplastic submucosa.
Fig. 11. Cross-sections through 3D RI reconstruction (GP method) of colon cancer (region 2), obtained using protocol $\boldsymbol{B}^{N\lambda }_{a}$: (upper row) two xy cross-sections selected at different depths and (lower row) corresponding xz images that visualize the same structures of interest (crypts) marked by blue (column (a)) and yellow (column (b)) arrows. The green arrow in (a) indicates the cross-section through the crypt within the mucosa while the muscularis mucosa is marked by red arrow.
Figs. 9–10 show results for region 1 of the colon cancer sample presented and analyzed in the same manner as those of experimental cell microphantom in Fig. 8 (Section 4.2.1). Figure 9 presents RI data reconstructed using DI reconstruction method while Fig. 10 the corresponding data for GP iterative method. The analysis performed for DI method was repeated for GP method to expose how the iterative algorithm affects the quality analysis when the considered measurement protocols are used.
The quantitative results that correspond to Fig. 9 and Fig. 10 were presented as the quality metrics in Table 5. In both cases (DI and GP methods) the improved quality of the reconstructed RI images is observed when protocols $\boldsymbol{A}^{1\lambda }_{u}$ and $\boldsymbol{B}^{N\lambda }_{a}$ are used, expressed in the noise level and thus, in SNR and CNR, as visible in Fig. 9–10 and Table 5. In this sense, the enhancement in parameters quantifying the quality of the obtained RI images agrees with the results acquired for experimental cell microphantom (Fig. 8 and Table 4). However, as shown in Table 5, the differences in noise level ($\sigma _{noise}$), and thus in SNR and CNR values, between all considered measurement protocols are less significant in case of GP reconstruction method due to improvement introduced by the iterative algorithm.
The imaging method used in this study allows to obtain a 3D reconstruction of the tissue RI distribution. It provides information about tissue’s histologic architecture and certain cytologic features in the specimen without performing any histochemical staining. The stained histopathological samples of 3-5$\mu m$ thickness are usually analyzed in 2D images. However, its interpretation in some cases can be challenging. For example, in the analyzed colon cancer, a tangential section through the crypt showing single cells allegedly not continuous with the crypt wall can be confusing. This is important as in some colon lesions the crypts lose their parallel arrangement. The confirmation of the presence of atypic cells in the lamina propria between the crypts on 3D images may be auxiliary in the identification of intramucosal colon carcinoma.
Here, taking advantage of the 3D RI imaging with improved quality obtained using protocol $\boldsymbol{B}^{N\lambda }_{a}$, in the NIR region, we provide a biological description of two different regions of the same colon cancer sample. In particular, for our investigations we selected the RI images reconstructed using GP iterative method and presented in Fig. 10(c,k) (region 1) and all images in Fig. 11 (region 2). The transverse (red arrow) and oblique sections (yellow arrow) through the crypts can be seen in Fig. 10(c) within the colonic mucosa. The walls of the crypts are formed abnormally by the multilayered epithelial cells (the nuclei are visible dark violet), and their lumens are filled with the mucin (visible as yellow mass). The groups of cells are present also between the cypts in the lamina propria. Such an image suggests the intramucosal migration of cancer cells and the presence of an inflammatory infiltration. Amorphous masses (ROI 1) on the left side may constitute the area of mucosal ulceration and destruction within the tumor. In area of the desmoplastic submucosa (blue arrow), among the vertically oriented fibers, the invasion of cancer cells along with stromal inflammatory response (ROI 2) is depicted in Fig. 10(c,k).
In the upper row of Fig. 11, the two xy cross-sections of 3D RI distributions obtained using protocol $\boldsymbol{B}^{N\lambda }_{a}$ (colon cancer sample, region 2) and selected at different depths of the sample are presented, while in the lower row, the corresponding xz cross-sections that visualize the same structures of interest marked by blue and yellow arrows.
The muscularis mucosa (red arrow) demarcates the mucosa (on the right) from the submucosa (on the left) that is apparent in Fig. 11(a). The longitudinal or oblique sections through the crypts characterized by the disordered architecture (green arrow) can be observed within the mucosa. These abnormalities are manifested by the crowded epithelial cells within the fused crypts. Moreover, in Fig. 11(a,b) the small groups and large masses of cells showing different degree of continuity with the crypts are visible in the lamina propria. In the oblique sections through the crypts, it can be seen that they are filled with the cells (blue arrow) or the mucin (yellow arrow) in Fig. 11(a) and Fig. 11(b), respectively. The cell pleomorphism is manifested by their various shape and size visible in both xy and xz images. The different degree of chromatin condensation is demonstrated by different values of refractive index (visible light to dark violet). Such cytologic features reflect the cancer cell atypia. The black areas in Fig. 11(a) visible within the muscularis mucosa may be the lymphatic vessels (red arrow). The invasiveness of colon carcinoma is confirmed by the crossing this barrier by cancer cells.
5. Conclusions
In this work we presented the holographic tomography technique, WIS-HT, which takes advantage of both angular and wavelength diversity in the NIR region. We have compared three experimental protocols differing in distribution of illumination angles and number of used wavelengths. In particular we examined single-wavelength (protocol $\boldsymbol{0}^{1\lambda }_{a}$) and multi-wavelength (protocol $\boldsymbol{B}^{N\lambda }_{a}$) annular scanning, and single-wavelength UDHS scanning (protocol $\boldsymbol{A}^{1\lambda }_{u}$). We found that all the approaches provide values of reconstructed RI distribution, also known from literature, with comparable contrast. On the other hand the SNR and CNR is higher in the multi-wavelength approach when compared to single-wavelength approach, even for the same number of projections used for reconstructions. The above findings were confirmed in numerical simulations as well as in experiments using PMMA micro-bead and cell microphantom. Furthermore, we show that this multi-wavelength NIR technique (NIR WIS-HT) is suitable to provide high quality RI distributions of relatively thick colon cancer sample. Finally, we show how to process the acquired data to obtain correct values of 3D RI distributions in both single-wavelength and multi-wavelength measurement scenarios. In particular, we presented the method for verification of the wavelength used in RI computations for multi-wavelength scenario and it was shown, that in the case of nearly linear dispersion of the material, the 3D RI distribution should be calculated using central illumination wavelength. Due to limited volume of the manuscript, we show only the strategy to obtain the correct RI distributions with optimized SNR in multi-wavelength HT. The problem of finding an angular and wavelength scanning strategy to optimize for example resolution in 3D or total imaging time will be reported in future research article.
Funding
Fundacja na rzecz Nauki Polskiej (POIR.04.04.00-00-1C1D/16-03, POIR.04.04.00-00-2070/16-00).
Acknowledgments
The research leading to the described results was carried out within the program of Foundation for Polish Science, co-financed by the European Union under the European Regional Development Fund. We would like to thank Marcin Sylwestrzak for his help in accelerating selected computations performed to obtain results presented in this work.
CRediT. Paweł Ossowski: Formal analysis, Investigation, Software, Visualization, Writing - Original Draft, Arkadiusz Kuś: Conceptualization, Methodology, Writing - Original Draft Wojciech Krauze: Data Curation, Methodology, Software, Writing - Review & Editing Szymon Tamborski: Investigation, Writing - Review & Editing Michał Ziemczonok: Resources, Investigation, Writing - Review & Editing Łukasz Kuźbicki: Resources, Writing - Original Draft Maciej Szkulmowski: Writing - Review & Editing, Funding acquisition, Project administration, Supervision, Małgorzata Kujawińska: Writing - Review & Editing, Funding acquisition, Project administration, Supervision.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010). [CrossRef]
2. K. Umemura, Y. Matsukawa, Y. Ide, and S. Mayama, “Label-free imaging and analysis of subcellular parts of a living diatom cylindrotheca sp. using optical diffraction tomography,” MethodsX 7, 100889 (2020). [CrossRef]
3. G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” American Journal of Physiology-Cell Physiology 295(2), C538–C544 (2008). [CrossRef]
4. M. Mir, Z. Wang, Z. Shen, M. Bednarz, R. Bashir, I. Golding, S. G. Prasanth, and G. Popescu, “Optical measurement of cycle-dependent cell growth,” Proc. Natl. Acad. Sci. 108(32), 13124–13129 (2011). [CrossRef]
5. F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31(2), 178–180 (2006). [CrossRef]
6. A. Kuś, W. Krauze, P. L. Makowski, and M. Kujawińska, “Holographic tomography: hardware and software solutions for 3D quantitative biomedical imaging,” ETRI J. 41(1), 61–72 (2019). [CrossRef]
7. D. Jin, R. Zhou, Z. Yaqoob, and P. T. C. So, “Tomographic phase microscopy: principles and applications in bioimaging,” J. Opt. Soc. Am. 34(5), B64–B77 (2017). [CrossRef]
8. A. M. Taddese, N. Verrier, M. Debailleul, J.-B. Courbot, and O. Haeberlé, “Optimizing sample illumination scanning in transmission tomographic diffractive microscopy,” Appl. Opt. 60(6), 1694–1704 (2021). [CrossRef]
9. W. Lee, D. Jung, S. Ryu, and C. Joo, “Single-exposure quantitative phase imaging in color-coded led microscopy,” Opt. Express 25(7), 8398–8411 (2017). [CrossRef]
10. A. B. Ayoub, A. Roy, and D. Psaltis, “Optical diffraction tomography using nearly in-line holography with a broadband led source,” Appl. Sci. 12(3), 951 (2022). [CrossRef]
11. P. Hosseini, N. Lue, Z. Yaqoob, R. R. Dasari, and P. T. So, “Self-reference line-dispersion interferometric microscopy,” Appl. Phys. Lett. 110(13), 131103 (2017). [CrossRef]
12. Y. Park, T. Yamauchi, W. Choi, R. Dasari, and M. S. Feld, “Spectroscopic phase microscopy for quantifying hemoglobin concentrations in intact red blood cells,” Opt. Lett. 34(23), 3668–3670 (2009). [CrossRef]
13. F. Montfort, T. Colomb, F. Charrière, J. Kühn, P. Marquet, E. Cuche, S. Herminjard, and C. Depeursinge, “Submicrometer optical tomography by multiple-wavelength digital holographic microscopy,” Appl. Opt. 45(32), 8209–8217 (2006). [CrossRef]
14. D. Bowman, P. Ireland, G. D. Bruce, and D. Cassettari, “Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments,” Opt. Express 23(7), 8365–8372 (2015). [CrossRef]
15. P. Hosseini, Y. Sung, Y. Choi, N. Lue, Z. Yaqoob, and P. So, “Scanning color optical tomography (scot),” Opt. Express 23(15), 19752–19762 (2015). [CrossRef]
16. C. Zuo, J. Sun, J. Zhang, Y. Hu, and Q. Chen, “Lensless phase microscopy and diffraction tomography with multi-angle and multi-wavelength illuminations using a LED matrix,” Opt. Express 23(11), 14314–14328 (2015). [CrossRef]
17. J. Jung, K. Kim, J. Yoon, and Y. Park, “Hyperspectral optical diffraction tomography,” Opt. Express 24(3), 2006–2012 (2016). [CrossRef]
18. T. Zhang, K. Unger, G. Maire, P. C. Chaumet, A. Talneau, C. Godhavarti, H. Giovannini, K. Belkebir, and A. Sentenac, “Multi-wavelength multi-angle reflection tomography,” Opt. Express 26(20), 26093–26105 (2018). [CrossRef]
19. W. Krauze, P. Ossowski, M. Nowakowski, M. Szkulmowski, and M. Kujawińska, “Enhanced QPI functionality by combining OCT and ODT methods,” Proc. SPIE 11653, 116530B (2021). [CrossRef]
20. V. T. Hoang, G. Stepniewski, K. H. Czarnecka, R. Kasztelanic, V. C. Long, K. D. Xuan, L. Shao, M. Smietana, and R. Buczynski, “Optical properties of buffers and cell culture media for optofluidic and sensing applications,” Appl. Sci. 9(6), 1145 (2019). [CrossRef]
21. M. Fluks, S. Tamborski, M. Szkulmowski, and A. Ajduk, “Optical coherence microscopy allows for quality assessment of immature mouse oocytes,” Reproduction 164(3), 83–95 (2022). [CrossRef]
22. P. Müller, M. Schürmann, and J. Guck, “The theory of diffraction tomography,” arXiv preprint arXiv:1507.00466 (2015).
23. N. Sultanova, S. Kasarova, and I. Nikolov, “Dispersion properties of optical polymers,” Acta Phys. Pol. A 116(4), 585–587 (2009). [CrossRef]
24. T. Gissibl, S. Wagner, J. Sykora, M. Schmid, and H. Giessen, “Refractive index measurements of photo-resists for three-dimensional direct laser writing,” Opt. Mater. Express 7(7), 2293–2298 (2017). [CrossRef]
25. M. Ziemczonok, A. Kuś, P. Wasylczyk, and M. Kujawińska, “3D-printed biological cell phantom for testing 3D quantitative phase imaging systems,” Sci. Rep. 9(1), 18872 (2019). [CrossRef]
26. J. Lim, K. Lee, K. H. Jin, S. Shin, S. Lee, Y. Park, and J. C. Ye, “Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography,” Opt. Express 23(13), 16933–16948 (2015). [CrossRef]
27. W. Krauze, “Optical diffraction tomography with finite object support for the minimization of missing cone artifacts,” Biomed. Opt. Express 11(4), 1919–1926 (2020). [CrossRef]
28. W. Krauze, P. Makowski, M. Kujawińska, and A. Kuś, “Generalized total variation iterative constraint strategy in limited angle optical diffraction tomography,” Opt. Express 24(5), 4924–4936 (2016). [CrossRef]
29. P. Narasimhan and R. E. Jacobs, “Neuroanatomical micromagnetic resonance imaging,” in Brain Mapping: The Methods (Elsevier, 2002), pp. 399–426.
30. V. A. Magnotta, L. Friedman, and F. Birn, “Measurement of signal-to-noise and contrast-to-noise in the fbirn multicenter imaging study,” J. Digit. Imaging 19(2), 140–147 (2006). [CrossRef]
31. J. Biswas, C. B. Nelson, V. M. Runge, B. J. Wintersperger, S. S. Baumann, C. B. Jackson, and T. Patel, “Brain tumor enhancement in magnetic resonance imaging: comparison of signal-to-noise ratio (snr) and contrast-to-noise ratio (cnr) at 1.5 versus 3 tesla,” Invest. Radiol. 40(12), 792–797 (2005). [CrossRef]
