A depth resolved hyperspectral imaging spectrometer can provide depth resolved imaging both in the spatial and the spectral domain. Images acquired through a standard imaging Fourier transform spectrometer do not have the depth-resolution. By post processing the spectral cubes (x, y, λ) obtained through a Sagnac interferometer under uniform illumination and structured illumination, spectrally resolved images with depth resolution can be recovered using structured light illumination algorithms such as the HiLo method. The proposed scheme is validated with in vitro specimens including fluorescent solution and fluorescent beads with known spectra. The system is further demonstrated in quantifying spectra from 3D resolved features in biological specimens. The system has demonstrated depth resolution of 1.8 μm and spectral resolution of 7 nm respectively.
© 2014 Optical Society of America
Spectral resolved imaging is a very powerful method to quantify cellular biochemical environment identifying chemical species and quantifying their concentration . By labeling cellular or tissue constituents with different fluorescent labels, multicolor imaging allows more precise determination of specimen morphology and composition; an example is the karyotyping of human chromosomes . The availability of many fluorescence probes with emission spectra sensitive to their chemical environment further allows intracellular mapping of biochemical states including ion concentration, pH, and voltage. Spectral resolved imaging was also shown to be an effective tool for studying protein-protein interactions based on resonance energy transfer measurement . Moreover, spectral resolved imaging is valuable for quantitatively identifying spectral signatures of endogenous biochemical species and to measure their concentrations in vivo. In clinics, spectroscopic measurement of cellular biochemistry can often provide information complementary to morphological analysis affording more accurate diagnosis, more precise demarcation of surgical margin, and more reliable evaluation of treatment outcome [4–6]. Spectral resolved imaging, of course, does not have to be based on fluorescent contrast. Many non-fluorescent analytes can be quantified based on their vibronic spectra using Raman imaging .
While bandpass filter wheel based spectral imaging is the most common and is very useful in applications where a few wavelength bands are sufficient for analysis, some more sophisticated applications often requires higher spectral resolution, i.e. hyper-spectral imaging. The goal of the spectrally resolved imaging is to record a 3D spectral cube which is composed of the pixels in 2D spatial dimension with its full spectral signature in spectral dimension. Hyper-spectral imaging has been demonstrated to be very powerful in studying tissue physiological and pathological states based on tissue endogenous fluorescent species that are often poorly understood prior to the study rendering filter based approach completely inappropriate [8, 9]. As another example, florescence resonance energy transfer (FRET) is often measured with bandpass filter at the donor and the acceptor emission wavelengths but cross-excitation and bleedthrough often require complex correction algorithm . However, the ability to measure the full spectra across the donor and acceptor emission bandwidth allows more efficient FRET measurement with fewer potential artifacts [3, 11].
Currently available hyperspectral imaging methods can be classified as scanning and non-scanning types. The scanning type methods can be further classified into three categories of spatial, spectral and optical path difference (OPD) scanning depending on the domains in which the scanning is performed. In the first case, the full spectrum is recorded for a point or a line with spectrally dispersive elements such as prism or grating and with 2D detector array. 4D data cube is sequentially recorded by scanning in 3D spatial locations . In the second case, the full spatial 2D field of view is imaged with 2D detector simultaneously and a single wavelength 2D image is sequentially recorded by scanning the wavelength with the tunable bandpass filters such as the acousto-optical tunable filter (AOTF), the liquid crystal tunable filter (LCTF), Fabry-Perot tunable filter and the angle tuned thin film bandpass filter . In the third case, spectral data is inferred after taking a sequence of 2D images by scanning OPD between the two emission beam paths in the interferometer. This category is termed as Fourier transform spectroscopy (FTS). There are different types of FTS depending on how OPD is scanned in the interferometer. OPD scanning can be implemented in various ways but the most commonly adapted mechanisms perform OPD scanning by either translating the mirror in one of the beam path in Michelson interferometer [7, 13] or rotating the whole Sagnac interferometer including the beam splitter and the two reflective mirrors with respect to the incoming beam  or translating the Wollaston prism in the birefringent FTS . Among these, Sagnac and birefringent type FTS have the advantages in stability because of its common path geometry. The non-scanning type FTS acquires 3D (x, y, λ) data cube in a single exposure without scanning at all. This types of spectrometer have the advantage in terms of temporal resolution but typically there is a tradeoff between spectral and spatial resolution and often they require extensive computation in post-processing. For example, the image mapping spectrometer (IMS) records 3D (x, y, λ) data cube in single shot by sharing the CCD detector for recording both spatial and spectral data simultaneously. However, the spatial resolution (or the field of view) is reduced as the spectral resolution increases .
For the depth resolved spectral imaging, the 3D imaging techniques such as the point scanning confocal microscopy or the two photon microscopy is most commonly used and can be combined with spectrometer based on dispersive elements . Alternatively, the depth resolved widefield imaging methods such as the temporally focused widefield two photon microscopy [17, 18] or the light sheet fluorescence microscopy  can be combined with the wavelength scanning spectrometer. Another approach, especially for single photon fluorescence imaging, is to use a structured light illumination (SLI). SLI approach has been demonstrated in the Sagnac interferometer based imaging FTS where the excitation light passing through FTS forms a SLI which encodes the depths information and is used to reject the out-of-focus photons from the emission light which pass through the same FTS . Also, SLI images based on phase-shifted sinusoidal illumination has been adapted to reject out-of-focus light in IMS .
In this paper, we describe a new implementation of depth-resolved hyperspectral imaging spectrometer based on SLI and FTS. Hyperspectral data cube is acquired with the Sagnac interferometer type FTS and the signals from out-of-focal planes are rejected by SLI based on HiLo microscopy. The current configuration has the advantage of achieving both high spatial and spectral resolution images. The overall system configuration is described in Section 2. The general working principle of the FTS based on Sagnac interferometer is described in Section 3. The proposed method of depth resolved FTS is mathematically derived in the Section 4. In section 5, the spectral background rejection with SLI is experimentally demonstrated with the fluorescent bead immersed in the uniform background. The depth-resolved hyperspectral 3D imaging is further demonstrated with a thin layer of cells immersed in the uniform spectral background and a kidney tissue section.
2. Overall instrument design of the imaging Fourier transform spectrometer
Figure 1 shows the schematic layout of the depth-resolved hyperspectral imaging spectrometer. Three diode-pumped solid states lasers (CNI laser) with emission wavelength of 473nm, 561nm and 660nm respectively were used as light sources, which can excite broad range of fluorophores. The three beams are combined into one collinear beam using the laser beam multiplexers (LM01-503-25, LM01-613-25, Semrock). Photobleaching effect is minimized by controlling passage of the excitation light with the optical shutter, OS1 (Ch-61, EOPC) which operates in synchrony with the exposure status signal of the camera so that the sample is exposed to the excitation light only when the camera is recording the emission light. The diffractive optical element (DS-033-Q-Y-A, HOLO/OR) split the beam into + 1 and −1 order and minimize the power loss by 0th order and other higher diffractive order beam. Since the beams spitted by DOE reaches to the focal plane of the objective via common path, they form a stable fringe pattern for SLI. The fringe period is 1.3μm at which the depth resolution is 1.8μm. The optical shutter, OS2 (Ch-61, EOPC) placed in one of the diffracted beam path blocks the beam for a uniform illumination (UI) and unblock the beam for a structured illumination (SI) which is formed by the interference of the two beams. The optical shutter is triggered by the external TTL signal and enables high speed switching between UI and SI. The dichroic mirror was used to separate the excitation beam from the emitted fluorescence signal and the emission filter right in front of the detector was used to block any stray excitation light reflected from the intermediate optical elements. The depth scanning is performed remotely by first forming the perfect 3D image of the sample in the focal space of the remote focusing objective and then by scanning the mirror in axial direction with piezo actuator . The hyperspectral image is acquired by recording the interferogram formed by the Sagnac interferometer which is subsequently processed to build the spectral cube of every pixels in two dimensional field of view.
3. Principle of imaging Fourier transform spectrometer based on Sagnac interferometer
In imaging Fourier transform spectrometry, each pixel of the 2D detector records simultaneously the spectrum of the source at the spatial location that is the conjugate point of the pixel. The emission light from the object first forms an intermediate image which is relayed to the 2D detector by the telescope. The interferometer placed in between the telescope splits the emission light into two paths and induces phase delay (OPD) in one of the beam paths. Then, the two beams are recombined at the 2D detector which records the time average intensity of the two electric fields that are phase delayed by the interferometer. Mathematically, these processes can be described as follows. The incident electric field upon the interferometer can be expressed asEq. (5), the first term is the dc term and the second term contains the spectral information. The intensity of source spectra, |A(x,y,ν)|2, can be readily recovered by cosine transform (the real part of the Fourier transform) of ac part of the interferogram. Mathematically, the interferogram is the autocorrelation function of the electric field. The inverse Fourier transform of the autocorrelation function of the electric field amplitude as a function of position is the spectrum, i.e., flux density as a function of wave number. This is known as the Wiener-Khinchine theorem .
Figure 2(a) shows the imaging Fourier transform spectrometer based on Sagnac interferometer. The basic configuration of the interferometer design is based on the commercial device (SpectraCube300, Applied Spectral Imaging). As shown in Fig. 2(a), the emission light from the intermediate image plane is collimated by the first lens and split into two paths which corresponds to the transmitted beam and the reflected beam at the beam splitter respectively. Subsequently, the two beams that are phased delayed relative to each other are focused to the sCMOS camera (PCO.EDGE 5.5, PCO) by the second lens. OPD originates from the fact that the two beam paths in the Sagnac interferometer are not parallel within the beam splitter and have different optical path lengths for a nonzero rotation angle of the Sagnac interferometer with respect to the position where the normal of the beam splitter is at 45° with respect to the optical axis . Optical path difference between the two beam paths can be expressed as Eq. (6), which is a function of the thickness (t) and the refractive index (n) of the beam splitter, the angle of the optical axis of the telescope on the beam splitter (β) and the rotation angle of the Sagnac interferometer (θ) with respect to the central position as shown in Fig. 2(a) .Eq. (7).Figure 2(c) shows the OPD scanning range for the spatial point on the optical axis. Since the spatial points on the detector off the optical axis have a non-zero input angle with respect to the optical axis after the first lens, the origin of the OPD scanning range shifts in proportion to the distance of the spatial point on the detector from the optical axis. Thus, each detector pixel along the horizontal direction experiences a OPD span that are shifted in proportional to the distance off the optical axis for the same rotational angle of the Sagnac interferometer.
The sampling process is performed in two steps. Figure 3 shows this sequential sampling process using a quad band emission filtered white light LED as an example. First, the 2D detector array capture the interferogram across the field of view for the given angle of θ at which OPD has a linear variation along the x direction due to the non-zero input angle of the ray from the off-axis spatial points while the OPD along the y direction is identical. Second, the zero OPD line is scanned across the field of view along x direction by rotating the Sagnac interferometer so that each pixel observes at least the single-sided interferogram. The double sided interferogram can provide a higher signal to noise ratio and induce minimal phase distortion compared to single sided interferogram at the expense of increased data acquisition time. For every pixel to observe the double sided interferogram, the zero OPD line has to be scanned more than half the width of the double sided interferogram from the right hand edge of the field of view and finish more than half the width of the double sided interferogram from the left hand edge of the field of view. The sampling periods in space and time are determined by the pixel size of the 2D detector array and the stepping size of the OPD shift respectively . To satisfy the Nyquist sampling theorem, a period of the fringe has to be sampled at least by two pixels of the 2D detector and the OPD stepping size has to be smaller than the half the wavelength. Therefore, the minimum detectable wavelength can be expressed as Eq. (8).Eq. (9) .
The raw interferogram is first band pass filtered by digital finite impulse response (FIR) filter with pass band between 400nm and 700nm. In case of biological sample, photobleaching is observed during the long range of OPD scanning and corrected by modeling the decaying dc values of interferogram with exponentially decaying function and subsequently dividing the raw interferogram with the exponentially decaying function. Digital bandpass filtering also has the similar effect of correcting the photo bleaching since the low frequency of exponentially decaying function is filtered out by the band pass filter. Afterward, the interferogram is phase corrected [26–28], apodized with modified Bartlett-Hann window, zero padded and then Fourier transformed by fast Fourier transform algorithm. The spectrum is then obtained by taking the absolute value of the result.
The actual OPD generated by the interferometer is found to slightly deviate from the theoretical estimation given by Eq. (6) for a number of reasons. Firstly, since the OPD is a function of the refractive index of the beam splitter, each wavelength see a different range of OPD depending on the dispersion property of the beam splitter material. Secondly, OPD is sensitive to the beam splitter angle and slight misalignment generates a huge error in the OPD estimation. To compensate these errors, the spectrometer is first calibrated with three color lasers at 473nm, 561nm, 660nm. The interferogram is first recorded with each color laser as a light source and then the wavelength is obtained using the OPD calculated using Eq. (6). Then the calibration factor is calculated by dividing the expected wavelength by the measured wavelength for each laser. Then, the OPD is rescaled by multiplying the calculated OPD with the average of the three calibration factors. This procedures can be summarized as follows.
After the initial calibration, the spectrum of the known emission wavelength fluorophores are measured and compared with their reference values. Figure 4 shows the raw interferogram and the corresponding spectrums of 6μm Yellow-Green fluorescent beads (F-8859, Molecular Probe), Rhodamine 6G solution (Sigma-Aldrich), 4μm Red fluorescent beads (F-8858, Molecular Probe). The samples are excited with the 473nm laser and the emission light is detected with the long pass dichroic mirror (FF495-Di02-25x36) and the long pass emission filter (BLP01-488R-25) for measuring the full emission spectrum.
4. Depth-resolved imaging Fourier transform spectrometry
Since the fringe formed by the interferometer is only determined by the light distribution in the input aperture of the interferometer, they form interferogram with the same modulation depth whether the light is from in- or out-of-focus plane. Therefore, the recorded interferogram contains both in-focus and the out-of-focus spectra information and the post-processed spectral cube from these raw interferograms would not provide depth-resolved spectral information. One of the methods for rejecting the spectral background signal is to use a structured light illumination (SLI) to encode the depth information in the (x, y, λ) spectral cube. The degree of modulation depth in the λ-plane contains the depth information.
So far, a class of depth-resolved imaging techniques based on SLI have been proposed to select a particular imaging plane and to reject out-of-focus background for standard wide-field single-photon microscopy [29, 30]. Of these methods, one effective approach we adapted is termed ‘HiLo microscopy’ which generates an optically sectioned image by post-processing the uniformly illuminated image (UI) and the structured light illuminated image (SI) . This algorithm is based on an assumption that 2D image can be divided into low frequency and high frequency contents. Since the high frequency contents are in-focus by its nature, the goal of using SLI is to encode the in-focus low frequency contents especially laterally zero frequency component with high frequency SLI. More specifically, the in-focused high frequency contents are extracted by high-pass filtering UI with a Gaussian shaped high-pass filter. The in-focus low frequency contents are extracted by low-pass filtering the absolute of UI subtracted by SI with the complementary low pass filter to the high pass filter. The cutoff frequency of the Gaussian filter is determined by the sinusoidal spatial frequency of the structured illumination. Subsequently, the optically sectioned image is obtained by combining the two with an adjusting factor so that the transition from low to high frequencies occur smoothly . HiLo microscopy has been widely used in the context of the background rejection for light-sheet microscopy [31, 32], the temporally focused widefield two photon microscopy  and the depth-resolved microrheology .
HiLo method can be applied for the spectral background rejection by first constructing the (x, y, λ) spectral cubes for both UI and SI and then post-processing each λ-planes from UI and SI with HiLo algorithm. Following the similar approach by Heintzmann et al. , we derived the mathematical formulation behind the spectral background rejection using SLI. The fringe pattern is imposed along the x direction by the interference of the two plane waves, which can be expressed as:Eq. (5), the interferogram observed by a pixel in the detector as the OPD is scanned can be expressed asEq. (12), the spectral cube of SI can be obtained asEq. (13) implies that each λ plane of the spectral cube preserves the depth information encoded by the structured light illumination. The procedure for recovering the depth resolved spectra is then similar to rejecting intensity background by SLI.
5. Experimental validation of spectral background rejection
5.1 Hyperspectral cellular imaging
We first demonstrate the hyperspectral imaging with the prepared slide containing the muntjac skin fibroblast cells (F36925, Invitrogen) stained with three different color fluorescent dyes. The filamentous actin is labeled with green fluorescent Alexa Fluor 488 phalloidin with emission peak at 519nm. Mitochondria are labeled with an anti-OxPhos Complex V inhibitor protein mouse monoclonal antibody in conjunction with orange fluorescent Alexa Fluor® 555 goat anti–mouse IgG with emission peak at 571nm. The spectral images is first acquired with the band pass filter as shown in Fig. 5(a) and then the hyperspectral image is taken for the area marked in red box in Fig. 5(a) and the result is shown in Fig. 5(b).
5.2 Spectral background rejection by SLI
We then demonstrate the spectral background rejection in a situation where a 6 μm yellow-green fluorescent bead is placed in the focal plane and uniform Rhodamine solution is placed in the out-of-focal plane. The sample is excited with both 473nm and 561nm laser to equalize the emission light from both colored samples. The emission light is detected with the quad-band dichroic mirror (FF410/504/582/669-Di01-25x36, Semrock) and the quad-band emission filter (FF01-440/521/607/700-25, Semrock). Figure 6(a) shows the spectral images for UI, SI and after the HiLo processing. In UI, the spectra from both the in-focused bead and the out-of-focus Rhodamine solution are detected, which demonstrates that there is no depth discrimination. In SI, the fringe pattern is visible only on the in-focused bead. After the HiLo processing the spectrum from the out-of-focus Rhodamine is rejected. Figure 6(b) shows the spectra of a point in the center of the bead. After HiLo processing, the out-of-focus spectrum is rejected.
Next, we obtained a spectral background rejected hyperspectral images with the same prepared cell sample used for Fig. 5 and the unifrom Rhodamine solution. As in the previous case, the cells are in-focus and the Rhodamine solution is out-of-focus. The samples are excited with the 473nm laser and the emission light is detected with the long pass dichroic mirror (FF495-Di02-25x36) and the long pass emission filter (BLP01-488R-25) for measuring the full emission spectrum. As shown in Fig. 7, the background signal from the Rhodamine is present over the broad emission wavelength range from 525nm to over 600nm with strongest contribution around 550nm. The HiLo processing removes this background and improves the contrast. The mitochondria which has similar emission wavelength with the Rhodamine is more clearly visible after the background spectrum is rejected.
5.3 Spectral background rejected hyperspectral tissue imaging
We further demonstrate the spectral background rejected hyperspectral imaging with a prepared slide of sectioned mouse kidney (F24630, Invitrogen). The sample is imaged with the same imaging condition for Fig. 7. The hyperspectral images are acquired for the 15μm thickness sample at 2μm step size for depth scanning. Figure 8 shows the 3D reconstructed volume images at the representative wavelengths for the uniform illuminated images (Fig. 8(a)) and the HiLo processed images (Fig. 8(b)). It is clear that the contrast of the images is improved after HiLo processing. Each spectral channel of the hyperspectral images for the very top layers of the sample are combined to produce a true color image as shown in Fig. 8(c). The contrast of the HiLo processed images are improved over the UI and the weak fluorescent features are more clearly visible.
This paper presents a depth resolved widefield hyperspectral imaging spectrometer based on imaging Fourier transform spectrometer and structured light illumination. While the Sagnac interferometer in the emission beam path does not have depth resolution, structured light illumination generated in the excitation beam path has been demonstrated to encode depth information in the recorded interferogram and the spectral background has been rejected with HiLo algorithm.
Since the OPD has a linear distribution across the field of view at any given instance in the Sagnac type imaging FTS, the zero OPD line has to be scanned across the entire field of view for each pixel at least to observe the single-sided interferogram. Currently, sampling interferogram is performed according to the Nyquist sampling criteria. Therefore, the total data acquisition time increases in proportion to the width of the field of view and can induce a significant photobleaching in case of biological sample. A recent development in the signal processing such as fast orthogonal search algorithm or compressive sensing technique may allow optical spectrum to be inferred with significantly fewer sampling of the interferogram while keeping the same spectral resolution [35, 36].
This work was supported by NIH 9P41EB015871-26A1, 5R01EY017656-02, 5R01 NS051320, 4R44EB012415-02, NSF CBET-0939511, the Singapore-MIT Alliance 2, the MIT SkolTech initiative, the Hamamatsu Corp. and the Koch Institute for Integrative Cancer Research Bridge Project Initiative.
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