1. Introduction

Imaging spectroscopy has rapidly developed within the past two decades. It has become a well-recognized technique in many fields, including biomedical optics, astronomy, environment monitoring, and other scientific and industry areas, as a powerful tool for object detection and identification with preferable accuracy [1,2]. The obtained data set which called “data cube” is a 3D matrix consisting of 2D spatial image and 1D spectral composition of each pixel of the image. To construct the 3D data cube by a 2D imaging sensor, a scanning operation is always needed. The conventional methods include spectral scanning by employing an optical band-pass filters wheel, or spatial scanning (pushbroom) in the along-track direction by using dispersive (or static interferometric) elements [3,4].

The above methods use fixed spectral resolution to produce a fixed data cube. To satisfy a variety of application requirements, the spectral range must be large and the resolution must be fine. This will result in a huge data for capturing, saving, transferring, and processing. Otherwise, the higher spectral resolution means the band of the filters or the input slit of the dispersive spectrometer should be narrower. In this way, only a small fraction of the spectral range (for filter-based spectrometer) or flux (for slit-based spectrometer) can pass through the system and be received by the detector. It will highly reduce the optical efficiency and signal to noise ratio of the instruments. However, for a specific application, the fine spectral resolution is not usually necessary, thus a majority of the spectral data should be discarded.

Although, the moving mirror Fourier transform imaging spectrometer (FTIS) [5] and electrically tunable filter imaging spectrometers, such as liquid crystal tunable filter (LCTF) [6] and acousto-optic tunable filter (AOTF) [7], have the spectral zooming capability. These apparatuses generally suffer from vibration, alignment difficulty, electrical noise, and heat generation. Consequently, considerable care is required for stable operation. Additionally, the optical throughput of the LCTF and AOTF is relatively low, and the incorporation of mechanical scanning components in FTIS typically increases the complexity and decreases the reliability of the system. Recently, Chen reported a dynamic imaging spectrometer based on a diffractive grating and a spatial filter (width-adjustable slit or transmission spatial light modulator) [8]. The drawbacks of this approach include spectral overlapping and limited optical efficiency of the spatial filter.

In this paper, we present a novel compact static birefringent imaging spectrometer with spectral resolution selection capability that can adapt to different application requirements and significantly reduce the size of the acquired data cube. The configuration employs two identical Wollaston prisms and has no slit. Without any internal mechanical or electronical scanning parts, it produces the interferogram and target’s image in the spatial domain which is localized coincident with the plane of a detector array. It also blends the advantage of a grating spectrometer and a Michelson interferometer: extremely compact, robust, wide free spectral range and very high throughput.

2. Theory

The optical schematic of the developed system is illustrated in Fig. 1 . It consists of fore-optics, polarizer P, two identical Wollaston prisms WP₁ and WP₂, analyzer A, imaging lens L, focal plane array (FPA). Light from the object is collected and collimated by fore-optics, and then incidents on P. The light emerging from P becomes linearly polarized at 45° to the optic axes of the Wollaston prisms. WP₁ and WP₂ split the incoming light into two equal amplitude, orthogonally polarized components with a small lateral displacement. After passing through A, the two component rays are resolved into linearly polarized light in the same polarized orientation and launched into the FPA. The interference pattern is thus superimposed on the image. This mode of data acquisition is the so-called “windowing” mode, in which the spectral imaging data cube is derived by the platform scanning the image across the interference pattern.

 

Fig. 1 (a) Schematic of the developed imaging spectrometer. (b) Ray trace of the beamsplitter constructed by two identical Wollaston prisms. The optic axes of the polarization elements are indicated by arrows and circles.

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The optical path difference (OPD) through the system is a function of the incident angle i, and can be described as:

It should be indicated that, the spectral resolution is not only determined by the spacing of the two Wollaston prisms, but also affected by the number of the detector pixels. If the interferogram captured by the detector were infinite in extent, the spectral resolution of this system would be unlimited; but since the pixel numbers is finite extent, only a portion of the interference pattern is able to sample. The result highest spectral resolution is given by:

3. Experiment and discussion

We carried out an experiment to demonstrate the validity of our method. The experimental setup is illustrated in Fig. 2 . In the developed scheme, each Wollaston prism is 17 × 17 × 7 mm³ with 5° internal wedge angle and made of calcite. A low-cost 1280 × 960 CCD camera with a lens of 50 mm focal length is used to take the interferogram. The total length of the proof system is less than 20 cm. A He-Ne laser is used to generate 632.8 nm monochromatic light being measured. In this way, not only the spectral resolution can be determined by checking the full width at the half maximum (FWHM) of the obtained spectral line, but also the lateral displacement introduced by the Wollaston prisms can be retrieved from the fringe frequency of the acquired interferogram.

 

Fig. 2 (a) Experiment setup of the developed imaging spectrometer. (b) Photograph of the core optics.

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The obtained interferogram is shown in Fig. 3 . It can be seen that the width of the interference fringe is changed with spacing s. The larger the spacing s, the narrower the fringe width is. The narrower fringe means larger OPD and higher spectral resolution.

 

Fig. 3 Interferogram captured by the described spectrometer with different spacing s between two Wollaston prisms.

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Figure 4 provides both the theoretical and experimental values of the lateral displacement introduced by WP₁ and WP₂ at 632.8 nm wavelength. The lateral displacement d changes from 0.13 to 0.75 mm when the spacing s varies from 0 to 20 mm.

 

Fig. 4 Theoretical and experimental values of the lateral displacement introduced by WP₁ and WP₂ at 632.8 nm wavelength.

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Figure 5 depicts the theoretical and experimental relationships between the spectral resolution and the spacing s. The spectral resolution at 632.8 nm wavelength changes from 985.1 cm⁻¹ to 151.1 cm⁻¹ (35.5 nm to 6.2 nm) when the spacing s varies from 0 to 20 mm. Compared with the theoretical values, the experimental results exhibit favorable accordance and the feasibility of the present idea is validated.

 

Fig. 5 Theoretical and experimental relationships between the spectral resolution and the spacing of two Wollaston prisms at 632.8 nm wavelength.

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The error difference between the theoretical and experimental results is mainly caused by the experimental error of the gap between WP₁ and WP₂. Although there is no precision tool used to adjust the parallelism of the two Wollaston prisms in the laboratory demonstration, the theoretical and experimental results were shown to yield accuracy better than 5%. This accuracy is quite enough for normal usage and can be highly improved by using a precision adjustment. It also proves that the proposed imaging spectrometer is extremely robust with such a simple, compact configuration. Note that the spectral resolution could be selected either by mechanically changing the spacing of the two Wollaston prisms, or by changing the refractive index of the gap between WP₁ and WP₂. The latter would be more stable.

We now consider about the optical throughput, free spectral range and wavelength accuracy of the presented imaging spectrometer:

(1) Optical throughput. The developed system has no slit. According to the optical throughput E calculation formula E = A$\Omega$, where A is the input aperture, $\Omega$is the solid angle of the filed of view (FOV) for the spectrometer [9]. For a similar spectral resolution, spatial resolution, and a same detector array, this advantage enables greatly higher throughput than a corresponding slit based spectrometer;

(2) Free spectral range. The dispersive spectrometer usually suffers from spectral overlapping of the diffractive grating. According to the diffraction grating equation, two spectral lines of different orders may overlap if their diffraction angles are equal. The spectral overlapping restricts the free spectral range of a dispersive spectrometer (e.g. first order 800nm spectrum of a grating will overlap the second order 400 nm spectrum. The free spectral range is 800 nm-400 nm = 400 nm). For a birefringent interferometer, there is no spectral overlapping. The spectral range is only limited by spectral response of the detector array and the crystal’s birefringence, and that is much larger than the dispersive spectrometer. (Birefringent crystals can be acquired that span wavelengths from 200 nm~14 µm [10] which are enough for most commonly used spectral passbands. For example, the useful spectral range of calcite crystal used in our experiment can be from 350 to 2300 nm.)

(3) Wavelength accuracy. Fourier transform spectrometer in general can yield spectra having arbitrarily dense spectral sampling intervals in contrast to the fixed wavelength interval binning imposed by dispersion spectrometer. Thus, for a given spectral resolution, the Fourier transform based instrument spectra can be interpolated, differentiated, and compared with spectra from other sensors more accurately than spectra from dispersion spectrometer [11]. A birefringent interferometer, based on a Wollaston prism, has been reported to determine wavelength of a He-Ne laser with an accuracy of 1 part in 10⁶ [12].

4. Conclusion

The theoretical operation and experimental demonstration of a compact static birefringent imaging spectrometer (BIS) with spectral zooming capability are presented. The proposed BIS is formed by cascading two identical Wollaston prisms. The main advantages of the proposed model are its compactness, static nature (i.e. no internal scanning parts), robust and low cost, yielding a simple Fourier transform BIS with spectral zooming capability. For different application requirements, the spectral resolution can be conventionally selected and extremely reduce the size of the data cube for capturing, saving, transferring, and processing. Furthermore, the presented sensor derives three advantages from the interferometer: high optical throughput, wide free spectral range and high wavelength accuracy.