1. INTRODUCTION

Hyperspectral imaging (HSI) is a growing field of investigation encompassing several advanced techniques to spatially identify the spectral signature of the various components in a given scene or sample. Uncountable applications of these methods cover a wide field of scientific investigations, such as remote sensing [1,2], pigment determination in biology [3], coastal ocean imaging [4], water analysis [5], agriculture [6], and cultural heritage and archeology [7], just to cite a few.

HSI is supposed to measure numerous and adjacent spectral bands and is often based on the combination of dispersive elements together with spatial scanning techniques. For instance, HSI in biological samples has recently been realized by using a spatial-scanning pushbroom probe [8]. More compact and performant HSI setups are continuously sought, the most demanded characteristics being the integration, compactness and robustness, the increased spectral resolution together with optimal spatial resolution, the removal of mechanical parts, increased field of view, attenuated losses, etc. Among the other solutions, wavelength filtering has emerged, where, in analogy with multispectral imaging, images are given back in a limited number of spectral bandwidths, this number being dictated by the discrete filters available. In this context, double filtering with two cascaded acousto-optic modulators has recently been shown to lead to spectral bandwidth compression and possible HSI applications [9]. Thermal HSI has been demonstrated in the mid and long infrared with a calomel acousto-optic tunable filter [10]. Liquid crystal (LC) based techniques have also been proposed, such as Fabry–Perot interferometers [11] or cascaded filters [12]. These techniques offer interesting perspectives; however, the full objective of HSI, that is, reconstructing the spectral features in each pixel of the image with a high spectral resolution, has still to be attained.

An alternative to the above-mentioned methods combines classical imaging with a Fourier spectrometer, the latter providing spectral information through an interferometric method [13]. In this approach, an optical temporal delay between two waves produces an interferogram for each detection point. Then, by continuously scanning the delay between the two waves, the whole spectrum is recovered through Fourier analysis. For multispectral imaging, an important criterion is the spectral FWHM bandwidth of the filters; here, the relevant parameter is the spectral resolution, which is inversely proportional to the temporal range. Conventional Fourier-transform hyperspectral imaging (FTHSI) instruments rely on Michelson or Mach–Zehnder interferometers, where mechanically moved mirrors provide the delay scanning. Sophisticated constructions enabled spaceborne and airborne devices for remote sensing applications [14,15], with excellent performances in terms of spectral resolution and spectral range. However, such mechanical systems suffer from a limited field of view, a need of high-cost translational stages to preserve the interferometric stability, and inherent sensitivity to vibrations and environment. Collinear interferometers, based on polarization-induced changes of the optical path between the ordinary and the extraordinary wave in birefringent media, such as calcite Wollaston prisms [16], might overcome some of these limitations by increasing compactness and simplicity. Nevertheless, such systems still rely on mechanical movements as the delay scanning is usually performed by displacing one of the prisms into the beam path.

LCs might be particularly suited in order to build polarization interferometers completely free of moving parts. Indeed, LCs are particularly attractive because of their high birefringence and the ability to change their optical axis through molecular reorientation in response to a low voltage or a weak magnetic field. Extensively studied for light manipulation and control [17,18], LCs have been, for instance, demonstrated as phase shifters for optical laser frequencies [19], microwaves [20], and THz [21] radiation. As a matter of fact, the principle of a LC-based Fourier spectrometer array was first proposed as early as 1990 [22] but only recently was it extended to HSI, probably thanks to the currently available technologies of low-cost and high-resolution cameras together with increasingly available computational power. Four monochromatic laser lines were used for calibration of a 100 μm thick LC cell in [23], whereas in [24] a 50 μm thick LC cell was investigated for compressive sensing. In both cases, the thickness of the birefringent medium limits the temporal range of the interferometer and a high spectral resolution cannot be actually reached. This drawback was mitigated in [24] by employing sophisticated numerical methods for pattern recognition but, although successful, both acquisition and computations were heavy and time consuming.

In this paper, we propose a new LC-based collinear polarized FTHSI system in which two cascaded LC cells are introduced for increased spectral resolution. One thick cell (200 μm) is dynamically driven with a voltage step for continuous scanning of the delay, whereas a thin static cell is used to introduce a temporal offset, allowing the zero of the temporal delay to be set precisely. Moreover, a subfemtosecond accuracy calibration of the introduced delay is achieved thanks to broadband spectral interferometry with femtosecond pulses. A general view of the proposed setup is shown in Fig. 1. This implementation, together with the calibration procedure, constitutes a conceptual breakthrough for practical applications of LC-based FTHSI, as it drastically improves the delay calibration procedure, usually performed with monochromatic laser lines [22,23]. A spectral resolution as good as $130{\mathrm{cm}}^{-1}$ (6 nm) over 400–1000 nm is achieved, which is a fourfold improvement compared to [23].

 

Fig. 1. Basic principle of the proposed LC-based Fourier spectrometer.

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These LC components are inserted in an imaging system with a field of view of 60° to perform HSI. A 3D volume of 13.3 M useful data points (111,216 points in the spatial dimensions, 120 points over the considered spectral bandwidth) are registered for a given sample. Examples of hyperspectral imaging are demonstrated with three representative samples permitting the potential of the technique to be evaluated in terms of its spectral performances, compactness, and robustness. The acquisition time for these demonstrations is 130 s.

The proposed device offers numerous advantages, actually combining benefits of colored filters in terms of simplicity with the high spectral resolution of a Fourier transform spectrometer. Furthermore, it is free of moving parts, compact, easily integrable, compatible with large aperture optics, low cost, and scalable in spectral range.

2. EXPERIMENTAL SETUP

The experimental setup is essentially composed of two cascaded planar-aligned nematic LC cells and a 2D detector, as represented in Fig. 2(a). The principle of the LC-based FTHSI can be summarized as follows. A first polarizer orients the initial polarization direction at 45° from the rubbing alignment of the LC cells and the two subsequent waves with orthogonal polarizations propagate with different velocities in the birefringent media. An analyzer, parallel to the first polarizer, enables beam recombination. The first and thick LC cell provides the electrically controlled temporal delay between the ordinary and extraordinary waves. The applied bias voltage ($V_b$) controls the molecular orientation, and thus the birefringence properties of the cell, through the relationship

 

Fig. 2. Experimental setup: (a) the FTHSI measurement configuration and (b) the calibration procedure. In the inset are shown the bias voltage step $V_b(t)$ applied to the thick cell together with the corresponding change of the LC average director tilt $\theta$ (solid line) and average extraordinary refractive index $n_e$ (dashed line). $n_e(t)$ depends on $\theta (t)$ according to Eq. [1] and $\theta (t)$ is related to $V_{b\max }$. In the experiment, $V_{b\max }=10\mathrm{V}$. In (b) a flip mirror is used to seed a femtosecond laser pulse train in the beam path instead of the white lamp.

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Driving the cell adiabatically enables scanning of the birefringence states but increases dramatically the acquisition time. In order to fasten the measurement, the cell is driven dynamically. To do so, by applying a bias voltage ($V_{b\max }$) onto the cell, LC molecules are brought out of equilibrium; then, the voltage is switched off, and LC molecules are dynamically driven back to their rest position. As the voltage step is applied, a fast scan of the temporal delay is obtained, from nearly zero (depending on $V_{b\max }$, here fixed to 10 V) to the maximum achievable value, following the molecular relaxation dynamics that brings the LC director back to its equilibrium position (see the inset of Fig. 2). This configuration constitutes an optical delay line that is continuously tunable, compact, and with no moving parts [25]. Furthermore, sub-fs temporal resolution is achievable with such a scheme. The tunable path delay is changed according to the incident angle on the LC cells. To preserve the uniformity of the optical path delay and the contrast of the measurement, the incident beam needs to be nearly collimated, which restricts the angular acceptance of the detector. It can be simply overcome by using double-nematic cells, as was done in [23], or compensation films for LC displays [17].

The maximum retardation undergone by the two waves is proportional to the cell thickness. For FTHSI, the spectral resolution is inversely proportional to the total temporal range and should be as narrow as possible. As a consequence, we decided to use a 195 μm thick LC cell. Note that with this implementation, the retardation between the two waves has the same sign whatever the applied voltage is. Only negative (or positive) delays are accessible. This issue could be resolved by cascading cells with similar thickness and crossed orientations, but at the expense of the absolute temporal range [25]. This is not done here, as not essential for the signal treatment. However, it is well known that because of anchoring conditions of the cell, for moderate bias voltage and thick cells, the medium cannot be seen as purely ordinary in both polarization directions, meaning that 0 phase retardation (or delay) cannot be reached while tuning the bias voltage between 0 V and $V_{b\max }$. This is a critical issue, as the field’s autocorrelation is not done properly and the Fourier analysis is then not able to retrieve the real spectral distribution. Consequently, we adjoin a second thin LC cell (25 μm), static, with crossed director orientation with respect to the thick one, and used as a temporal offset. As shown below, this is sufficient to reach the 0 delay while preserving a large temporal excursion.

The full experimental setup is pictured in Fig. 2. The sample, on a 3-axis translation stage, is illuminated by a white light source (calibration lamp from Ocean Optics) and placed between two microscope objectives for relay imaging. The field of view is approximately 60°. LC cells are made by using 0.7 mm thick, $25\mathrm{mm}\times 25\mathrm{mm}$ transverse size, glass substrates over which an indium-tin-oxide (ITO) layer is deposited to allow the application of a bias voltage. A thin film of polyvinyl alcohol (PVA) is deposited over the ITO and rubbed in order to favor the planar alignment of the LC molecules (LC director is parallel to the confining surfaces of the cell). Adequate-sized spacers are then glued between two substrates and the commercial nematic mixture E7 (Merck) is finally inserted in the cell gap. The cells’ clear aperture is 20 mm. Only the first thick cell, providing a variable retardation path for the incoming beam, is electrically addressed with a sinusoidal AC voltage (frequency 1 kHz). The transmission of the cells is, respectively, 72% (195 μm) and 75% (25 μm), and limited by Fresnel losses on the uncoated substrates and absorption in the ITO layers. Including losses on the polarizers, the total delay-line transmission is 40%. An improved cascaded cell design (for instance, the two cells sharing a substrate) would raise this value. Finally, the detector is a fast CCD camera (PHOTRON, $512\mathrm{pixels}\times 512\mathrm{pixels}$) enabling kilohertz acquisition rate. The optical delay line can be positioned as close as possible to the detector and the CCD detector matches the image plane. The measured spectral bandwidth, limited by the polarizers and CCD, is 400–1000 nm.

As explained above, the cell is driven dynamically by turning off the bias voltage $V_{b\max }=10\mathrm{V}$. The images are acquired during the transient reorientation of the LC molecules back to their initial position (inset of Fig. 2). However, the dynamical relaxation is not easily predictable and has to be calculated [17,23]. Given the strong dependence of the experimental birefringence of the LC mixture to various parameters such as effective cell thickness and room temperature, we introduce here an accurate in situ calibration of the induced temporal delay. This calibration procedure increases the fidelity of the signal treatment, while no assumption is needed because the average director orientation in both cells is directly measured. Broadband spectral interferometry is used to perform this experimental delay calibration.

3. CALIBRATION BY GROUP DELAY RETRIEVAL

In order to perform the calibration procedure, the sample is removed and a femtosecond laser pulse train is seeded in the beam path instead of the white lamp. Then, the CCD camera is replaced by a spectrometer to spectrally resolve the interference pattern between the ordinary and extraordinary components of the pulse, as indicated in Fig. 2(b). A Fourier transform of the registered spectrum enables the calculation of the experimental group delay between the two fields [26]. Indeed, a given configuration of the LC-based delay line provides a given group delay $\tau$ between the two polychromatic waves. The detected spectral intensity can be written as

The femtosecond source is a Femtofiber PRO IRS (Toptica Photonics) oscillator delivering 40 fs pulses, at 1570 nm, with a 200 mW average power. The repetition rate is 80 MHz. The pulses are frequency-doubled in a 0.25 mm BBO crystal. The resulting spectrum presents 60 nm bandwidth at full width half-maximum (110 nm at $1/e^2$) and is centered at ${\lambda }_0=770\mathrm{nm}$. The delay line is then calibrated in the same experimental conditions as for FTHSI measurement. The bias voltage ($V_{b\max }=10\mathrm{V}$) applied to the thick cell is turned off and the interference spectrum is logged every 8 ms, with an integration time of 2 ms. The acquisition lasts 140 s to allow the LC cell molecules to reorient toward their initial position.

The resulting interference spectra versus acquisition time are plotted as a 2D map, as shown in Fig. 3(a). The spectral pattern is resolved all along the measurement, demonstrating that the acquisition rate is sufficient for this cell. As expected, the highest number of spectral fringes (e.g., the larger group delay) is registered at the end of the acquisition. The LC molecules are then back to their anchoring conditions and the medium is extraordinary with its optical axis along the vertical polarization direction. Thanks to the offset cell, the overlap (0 phase retardation) is reached: all the spectral components are coherently added and the complete laser spectrum is measured. The spectrogram indicates that the 0 delay occurs 480 ms after the beginning of the molecular reorientation.

 

Fig. 3. Calibration of the FTHSI delay line. The bias voltage of 10 V is shut down at $t=0$. (a) The interference spectrum recorded regularly (every 8 ms) as a function of time. (b) The retrieved group delay between the two polarization states as a function of acquisition time.

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The complete delay evolution is then calculated with a Fourier transform of the interferogram and plotted in Fig. 3(b). A 0.3 fs temporal resolution per acquisition step is measured for the steeper part of the curve. Successive acquisitions establish that the error bars are small ($<0.1\mathrm{fs}$) thanks to the good resolution of the spectrometer (0.3 nm) and the rapid acquisition limiting external perturbations influence (vibrations, temperature changes, etc.). For a given lab temperature, the calibration was found reproducible ($\pm 0.2\mathrm{fs}$) on a day-to-day basis and consequently is needed only once. However, it is well known that variations of the temperature affect the birefringence of the LC mixture. For instance, an increase of the temperature from 19° to 21°C induces a reduction of $\mathrm{\Delta }n=n_e-n_o$ by a factor 0.95 for E7 [17]. To accommodate such variations, the system can be precalibrated for various temperatures.

Finally, the maximum positive group delay, measured for a central wavelength ${\lambda }_0=770\mathrm{nm}$, is ${\tau }_{\max }=130\mathrm{fs}$. Consequently, the spectral resolution of the following FTHSI measurements is estimated to $\mathrm{\Delta }\sigma =130{\mathrm{cm}}^{-1}$ ($\mathrm{\Delta }\lambda =6\mathrm{nm}$).

4. MEASUREMENTS AND ANALYSIS

To proceed to FTHSI measurement, the sample is positioned in between the objectives, illuminated by the white lamp, and imaged onto the CCD camera. As the control LC cell is driven dynamically, we need to acquire the images with a sufficiently fast acquisition rate. The chosen frame rate is 125 frames per second (acquisition period: 8 ms), according to the calibration procedure. The image size was fixed to $512\mathrm{pixels}\times 218\mathrm{pixels}$, which allowed the chosen acquisition rate on the camera. During the acquisition, the successive images are captured by the CCD while tuning the optical path delay, e.g., during the transient reorientation of the LC molecules after turning $V_{b\max }$ off from 10 V to zero. The acquisition time lasts 131 s, which was dictated by the relaxation time of the LC reorientation dynamics. The spectral information is then encoded into a spatial interferogram. The detected signal from one pixel can be written as

The one-sided interferogram registered for one pixel is shown in Fig. 4(a). The inset displays a zoom of the first ten seconds. The chirp of the interferogram is a reminder that the acquisition time and the temporal delay do not evolve linearly. The overlap (e.g., 0 delay) can be identified as a maximum constructive interference and enable us to make the interferogram symmetric. The acquisition time (seconds) then needs to be converted to delay (femtoseconds). To do so, we first sample the calibration curve of Fig. 3(b) with a constant delay step. $\mathrm{\Delta }t=0.4\mathrm{fs}$ is chosen. According to the Nyquist criterion, this value fixes the minimum measurable wavelength (${\lambda }_{\min }$). Here, ${\lambda }_{\min }=220\mathrm{nm}$. The signal is finally plotted as a function of the delay with a constant step size. Figure 4(b) shows the resulting interferogram.

 

Fig. 4. Interferogram measurement and analysis. The bias voltage of 10 V is shut down at $t=0$. (a) The one-sided interferogram measured for one pixel of the camera as a function of time over the full acquisition span. The inset is a zoom of the ten first seconds of acquisition. (b) The reconstructed interferogram as a function of the retardation time between the two polarization components of the incident light. The baseline is indicated (dashed).

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The signal is finally processed through the inverse Fourier transform. The retrieved spectral resolution is plotted in Fig. 5(a). $\mathrm{\Delta }\sigma =129{\mathrm{cm}}^{-1}$ is in agreement with our expectations. In a first step, the white lamp spectrum, called reference, is recovered alone [Fig. 5(b)], weighted by the spectral sensitivity of the detector. ${\lambda }_{\min }$ is indicated, as well as the actual measured bandwidth, and limited by polarizers and CCD. A bandpass filter is then inserted in the beam path in order to check the validity of the measurement and analysis. As can be appreciated from Fig. 5(b), the retrieved spectrum shows a faithful reconstruction of the filtered bandwidth.

 

Fig. 5. (a) Retrieved spectral resolution as a function of the wavelength. (b) The retrieved spectrum of the calibration lamp without (higher blue curve) and with (lower red curve) a bandpass filter. The hatched area indicates the detected spectral bandwidth. The spectral cutoff ${\lambda }_{\min }$ is also indicated.

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5. HYPERSPECTRAL IMAGING

Examples of FTHSI were performed with three representative samples. In each case, the control LC cell is driven by switching off the bias voltage $V_b$ from 10 V to zero, then by acquiring the images regularly during the LC molecular relaxation dynamics, and finally by Fourier processing the data as explained in the previous section. The procedure reconstructs the spectrum for each part of the image and thus leads to the complete spatial dependence of the spectral transmission of the sample. The spectra can be normalized by the reference spectrum from the lamp if needed. As a consequence, monochromatic images can be presented and the hyperspectral data cube can be reconstructed as well.

As a first test, a beam splitter pellicle BP145B1 from Thorlabs was imaged. This pellicle has no particular spectro-spatial dependence; however, it presents regular spectral modulations in transmission with a period around 30 nm. The modulations contrast is about 25%. To emphasize the retrieved FTHSI spectral modulations, the background spectrum is subtracted after Fourier analysis. The results are shown in Fig. 6. The hyperspectral data cube clearly exhibits regular spectral fringes. A good agreement is obtained by comparison with the data provided by the furnisher, hence validating the spatial and spectral accuracy of the proposed hyperspectral imaging system.

 

Fig. 6. FTHSI of a beam splitter pellicle BP145B1 from Thorlabs. (a) The hyperspectral data cube. (b) Bottom: the reconstructed spectrum. Top: the background spectrum is subtracted and the retrieved spectral transmittance of the pellicle [red, from the ZOI indicated in (a)] is compared to the data provided by the furnisher (green).

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A biological sample was then studied. The reconstructed hyperspectral data cube of a giant chromosome can be seen in Fig. 7. Monochromatic images at 549, 646, 706, and 855 nm are also presented together with the normalized spectral transmission extracted from various zones of the chromosome. The fidelity of the FTHSI retrieval can be clearly appreciated.

 

Fig. 7. FTHSI of a giant chromosome. (a) The hyperspectral data cube. (b) The spectral transmission extracted from chosen parts of the picture. The spectra are normalized with respect to the reference and the color of the lines refers to the color of the ZOI in (a). (c) From the data cube, monochromatic views of the sample can be reconstructed.

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Finally, we performed FTHSI of a liquid sample, a homemade cell containing water mixed with olive oil. The oil drops are clearly visible, as shown in Fig. 8. Recovered transmitted spectra from the water and a drop are compared, and the chlorophyll absorption around 650 nm can be measured. This is emphasized by the monochromatic image extracted at 650 nm.

 

Fig. 8. FTHSI of a mixture of olive oil and water. (a) An image of the sample. The white line limits the analyzed area. (b) The transmitted spectra. The color line refers to the color of the ZOI in (c). (c) A monochromatic image (650 nm) of the selected area.

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6. CONCLUSION AND PROSPECTS

To conclude, we have demonstrated a compact FTHSI device where two cascaded nematic LC cells provide the tunable path delay. The efficient implementation of a thick ($\sim 200\mathrm{\mu m}$) cell associated with a thin (25 μm) offset cell enables the spectral resolution to be improved, down to $130{\mathrm{cm}}^{-1}$ (6 nm) over the 400–1000 nm spectral range. Furthermore, broadband spectral interferometry is used for accurate, in situ, temporal calibration. This is a critical point for LC-based FTHSI fidelity as it provides an accurate calibration of the optical delay line for the actual beam path. The delay evolution and the achievable sampling rate are precisely determined and no assumption about the LC cell is needed. The method improves the accuracy of the FTHSI reconstruction. As representative examples, hyperspectral imaging over the 400–1000 nm spectral range is successfully realized for a pellicle, a giant chromosome, and a liquid sample.

By comparison with the recent publication of Hegyi and Martini [23], where a single LC cell, dynamically driven as well, was used in a FTHSI device, significant improvements have been demonstrated. The cascaded LC cell scheme provides a fourfold improvement of the spectral resolution. Furthermore, the broadband calibration enabled the need to be pointed out for LC-based setups of a small temporal offset to proceed to the complete spectral reconstruction through Fourier analysis. The increased precision (0.1 fs) of the proposed calibration compared to the procedure with a monochromatic laser leads to a better accuracy and sensitivity to potentially impact environmental changes. Finally, the double-nematic structure used in [23] can be easily adapted to our method.

It must be noted that the performances of the system could be improved further. In particular, imaging of other polarization directions can be achieved by a simple rotation of the polarizers. The acquisition time can be significantly reduced by applying ascending voltage steps or ramps. Higher resolution could be achieved by cascading additional cells with opposite pre-tilt conditions in order to simultaneously increase the field of view. As a matter of fact, LC technologies are known to provide a large field of view (LCD, [17]). This property, combined with the almost unlimited aperture of LC cells, might increase dramatically the accessible etendue compared to traditional FTHSI instruments. Furthermore, scalability to higher wavelengths is straightforward. Finally, the compactness of the proposed technology allows its integration in microscopes or movable supports to be possible, thus opening the way to future implementations for numerous and different application fields.