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In this work, we present a close-range ultraviolet imaging spectrometer with high spatial resolution, and reasonably high spectral resolution. As the transmissive optical components cause chromatic aberration in the ultraviolet (UV) spectral range, an all-reflective imaging scheme is introduced to promote the image quality. The proposed instrument consists of an oscillating mirror, a Cassegrain objective, a Michelson structure, an Offner relay, and a UV enhanced CCD. The finished spectrometer has a spatial resolution of 29.30μm on the target plane; the spectral scope covers both near and middle UV band; and can obtain approximately 100 wavelength samples over the range of 240~370nm. The control computer coordinates all the components of the instrument and enables capturing a series of images, which can be reconstructed into an interferogram datacube. The datacube can be converted into a spectrum datacube, which contains spectral information of each pixel with many wavelength samples. A spectral calibration is carried out by using a high pressure mercury discharge lamp. A test run demonstrated that this interferometric configuration can obtain high resolution spectrum datacube. The pattern recognition algorithm is introduced to analyze the datacube and distinguish the latent traces from the base materials. This design is particularly good at identifying the latent traces in the application field of forensic imaging.
© 2016 Optical Society of America
1. Introduction
Hyperspectral imaging (HSI) detection is an important kind of nondestructive methods applied in many field including material science, biology [1], cultural heritage [2], and forensic science. For forensic applications, HSI is mainly used for latent image analysis and trace detection, especially for traces of blood [3], explosives [4], fingerprints [5], and pen inks [6]. In ultraviolet (UV) band, imaging technique has been utilized to photograph various latent residues [2,7 ]. UV HSI method using either dispersion or interferometric configuration has been of great interest [1,8 ]. This method combines advantages of image identification and spectral analysis.
A typical example of dispersion configuration is prism-grating-prism imaging spectrograph, which was first proposed by Aikio et al. in 1997 [8]. Using this structure, a first UV (250~450nm) hyperspectral system was installed in China by Themis Vision Systems in 2010 to help with studies in forensic science, including document examinations and fingerprint analysis [9]. However, such configuration uses an entrance slit aperture which limits the amount of radiometric throughput, and its spectral line had intrinsic bend phenomena due to dispersion. Therefore, the dispersion configuration of HSI is limited for forensic analysis, especially in the case of low illumination or low signal-to-noise ratio (SNR).
The interferometric configuration usually includes a Michelson structure, which is implemented by either a time-modulated interference structure [1] or a spatial-modulated interference structure [10]. Besides, a new type of scanning Fabry-Pérot interferometer in UV band was proposed by Caricato et al. in 2014 [11]. It uses a movable cavity to change the optical path which is similar with the time-modulated Michelson interferometer. The time-modulated interference structure needs very precise motion control mechanism, which is prohibitive and complex for our applications. The imaging interferometer with spatial-modulated interference structure was first presented in the High Étendue Imaging Fourier Transform Spectrometer system by Horton in 1996 [10]. In 2001, Posselt et al. implemented this HSI configuration on the small satellite terrestrial remote sensing missions under ESA's project [12]. The relatively simpler structure is the advantage of this configuration. Until now, this configuration has not been adopted for UV band imaging interferometer.
Based on this spatial-modulated interference structure, we aim to design a close-range ultraviolet imaging spectrometer (CR-UVIS) for latent image analysis applications. In order to achieve this goal, the ideal imaging device should meet the following requirement: (a) the spatial resolution of the captured image should be less than 0.1mm, so that the very small detail of the target can be illustrated; (b) the obtained spectra should cover both near and middle range of UV; (c) sufficient amount of wavelength samples can be provided over the obtained spectra, so that the reflective spectrums of different materials can be discriminated and identified.
Next, we present the design of the instrument and the implementation details.
2. Instrument design
2.1 Overview
For the UV band, the traditional transmissive optics generates chromatic aberration, which severely reduces the spatial resolution. To address this issue, we adopt a scheme of all-reflective optics except a Michelson structure. The layout scheme of the proposed imaging spectrometer is depicted in Fig. 1 . The incident light beam is first reflected by a flat beam-folding oscillating mirror, which is used to scan the target surface. In addition, a multilayer dielectric film is coated onto this mirror to filter out the visible light. Next, a Cassegrain objective receives the beam and then focuses it onto the two intermediate image planes, which are the two mirrors in a Michelson structure. Subsequently, an Offner relay optics system mixes these two intermediate images and focuses on the focal plane array of a CCD (FLI PL4710, MultiPix Imaging, UK). The response of the CCD is UV enhanced in the range of 200~400nm. The actual working band of the dielectric film is found to be 240~370nm by a separate measurement. This range can be considered as the working band of the instrument. Thus, the proposed spectrometer has strong spectral response over the near and middle UV.
Fig. 1 Layout scheme of the proposed imaging spectrometer. The subfigure shows the wedge-shaped Michelson structure.
The CCD has a 1024 × 1024 UV detector array with 13μm pixel spacing. A test of imaging range shows that the lateral line-of-sight is 30mm on the target plane. At the designed object distance, which is 700mm, the field of view (FOV) of the camera is 42.85mrad. Thus, the FOV of each pixel is approximately 0.042mrad, and the spatial resolution (or the projection of one pixel on the target plane) is 29.30μm. This resolution is sufficient for our application and excels the spectrometers with similar design [12]. The chromatic aberration induced by the Michelson structure is estimated to be less than one pixel, which proves the advantages of the all-reflective optics. In practice, we find that no apparent chromatic aberration can be observed.
The interferogram is generated by slightly tilting one of the mirrors (Mirror M2 in Fig. 1) in the Michelson structure. As shown in Fig. 1, the dotted line (M1') presented in the left-bottom subfigure represents image of Mirror M1 in the beam-splitter BS. Thus, the M1' (dotted line) and the M2 (solid line) forms a wedge of small angle α and generates equal thickness fringes. These fringes are equidistant straight lines parallel to the apex of the wedge and are imaged on the focal plane of the CCD as an interferogram.
We aim to obtain approximately 100 wavelength samples over the range of 240~370nm. Here, we present the procedure to determine the wedge angle α. Due to the symmetric interferogram, the half of interferogram dimension is N = 512 pixels. According to the Nyquist-Shannon sampling condition, in maximum 256 interference orders can be sampled. In order to resolve the interferogram generated by the shortest wavelength, which is 240nm, the upper limit of the optical path difference (OPD) is ∆ max = 240nm × 256 = 61440nm (or 61.44μm). According to α max = tan−1[∆ max/(2Nd px)], where d px = 13μm is the CCD pixel spacing, the maximum wedge angle is α max = 0.26° (or 4.6mrad). As the shortest wavelength is 240nm, the maximum wavenumber ν max is 41666.7cm−1 and the wavenumber resolution is given by δν = ν max/N = 81.4cm−1. In this case, the wavelength sample which corresponds to 370nm (27027.0cm−1 in wavenumber) is near the 332th point in spectrum dimension. We can easily calculate that the maximum wavelength samples within 240~370nm is 181 points (332th~512th point in spectrum dimension). This is the case of maximum spectral resolution. However, higher spectral resolution (larger OPDs) leads to lower SNR [13]. In practice, we set the wedge angle α = 0.14° (or 2.4mrad) to achieve better SNR and approximately 97 wavelength samples within 240~370nm (172th~268th point in spectrum dimension).
In summary, the finished spectrometer has a spatial resolution of 29.30μm on the target plane; the spectral scope covers both near and middle UV band; and can obtain approximately 100 wavelength samples over the range of 240~370nm.
2.2 Working mechanism
To acquire interferogram, each column of the target image needs to occupy each possible position over the wedge (or column of pixels on CCD) once. Each column of the target image then interferes with itself for each one of the phase differences that the wedge allows. In our case, the CCD has 1024 column of pixels. Thus, to achieve the maximum spectral resolution, for any column of the target image, 1023 extra exposures are needed. Since the exposures of all the columns of CCD are carried out in parallel, the total number of exposures equals to the number of columns needed to cover the target surface plus 1023, as shown in Fig. 2 . To do so, the oscillating mirror shifts the target image on the CCD plane laterally for one pixel per snapshot. This process is repeated until the target surface is covered totally. This scan is controlled by a computer, which coordinates the motor motion of the oscillating mirror and the exposure of the CCD.
The interferogram keeps static during the scan. Thus, the interferogram of one target image column can be reconstructed by taking one pixel column from each image, as shown in Fig. 2. The result of this reconstruction is called the interferogram datacube.
For example, a 20mm wide target needs to be scanned. On the CCD plane, the target covers 680 pixel columns. To achieve the maximum spectral resolution, 1023 extra exposures are needed, so that the total exposure number is 1703. The average exposure time is about 500ms and the motor rotation takes about 50ms. Thus, the total scan time is about 937s (15 minutes) in this case.
Since the data acquisition and interferogram reconstruction is controlled by a computer, the whole process is quite efficient.
3. Spectral calibration
The reconstructed interferogram datacube has two spatial dimensions and one interferogram dimension, given as I(x, y, δ). A Fourier transformation can be applied to the interferogram dimension of this datacube and can convert this datacube into a spectrum datacube, given as I(x, y, ν), in which the ν is wavenumber.
However, the wavenumber (or spectral) calibration is needed to determine the actual wavelength for each wavelength sample in the obtained spectral curve. Then, the actual spectral resolution of the instrument can be calculated and can indicate whether the instrument achieves the design goal. The wedge structure guarantees the linear distribution of the phase difference in the obtained interferogram, and the wavenumbers of the spectral samples are also linearly distributed. Therefore, to determine the actual wavelength of a single wavelength sample is sufficient for spectral calibration. We chose a high pressure (HP) mercury lamp as the spectrum reference, which has a prominent 365.0nm characteristic peak (27388.3cm−1 in wavenumber) [14]. Additionally, the other characteristic peaks in the emission spectrum of HP mercury lamp are utilized to validate the calibration result.
A uniform, white ceramic sample is illuminated by the HP mercury lamp. As the sample is homogeneous, all the columns are equal in reflective spectra and all OPD changes can be achieved in one snapshot. The captured interferogram is shown in Fig. 3(a) .
Fig. 3 Spectral calibration results. (a) Interferogram on white ceramic illuminated by a HP mercury lamp. (b) Spectra of HP mercury lamp, the curve were normalized to arbitrary units.
Then the spectrum is calculated by spectral inversion algorithm based on the Fourier transformation. The qualitative comparison of normalized spectra from the same line in Fig. 3(a) is depicted in Fig. 3(b). It can be found that the spectra of HP mercury lamp have a prominent characteristic peak at 365.0nm. The corresponding position of 365.0nm was used in wavenumber calibration. Besides, the peaks near 313.2nm and 334.1nm have discernible but weaker responses. We used the chirp z-transform algorithm to increase the sampling rate in a narrow frequency range of each characteristic peak in Fig. 3(b). This method is efficient for reducing the Fourier transform complexity in a fine sampling rate [15]. In this way, the wavenumber resolution δν can be calculated as 155.67cm−1, and other two peaks are used to verify this result. It shows that the spectral resolution varies with the wavelength, which is 0.90nm at 240nm and 2.13nm at 370nm.
The calibration results of the imaging spectrometer then give correct wavelengths to the spectrum dimension of the spectrum datacube I(x, y, ν).
4 Experiments and discussion
In this section, we present the experiment setup and the data analysis. The results of the data processing are discussed.
4.1 Experiment setup
In order to validate the proposed instrument, we used three different approaches to analyze a thermochromic pen ink sample, and compared the measurement results. The first approach is to capture the image of the sample by a RGB color CCD and a broadband UV light source (a deuterium lamp). The second approach is to capture the image of the sample by a UV enhanced CCD and two narrowband UV light sources. These two approaches are widely-used for document analysis applications [16,17 ]. The third approach uses the proposed instrument with a broadband UV light source (a deuterium lamp).
The experiment setup is shown in Fig. 4 . All the light sources can be installed in a dark room to ensure a steady sloping illumination condition. The CCD cameras and the imaging spectrometer can be installed on top of a sample holder and aligned to the normal of the target surface. The sample holder, which is a vertically-adjustable stage, is utilized to align the target surface to the focus planes of CCD cameras and the imaging spectrometer. This setup allows us to switch the light sources and cameras easily for three different measurement setups. Figure 4 shows the setup instance of the broadband UV light source and the imaging spectrometer.
The performance of the CR-UVIS was evaluated by analyzing a forged handwriting. Originally, a “10” was written on a white printing paper by a blue thermochromic pen (Snowhite G-031M, pen#1). Later, we used a plastic eraser to erase the number “0”. Rubbing the paper surface generated heat and raised the temperature. The blue ink turned white when this temperature is above a threshold. Note that this thermochromic effect is different from removing the ink entirely from the paper surface [18]. Most of the ink still remains on the paper surface. Then, a“47” was written with a different blue thermochromic pen (Pilot FriXion LFB-20EF-L, pen#2), where the “|” stroke of “4” was written right on top of the original number “1”. The sample represents a typical forged handwriting.
4.2 Experiment results of color CCD camera and broadband UV light source
Firstly, the handwriting is analyzed by a color CCD camera. The image in Fig. 5(a) is captured by the CCD camera with a white LED light source. The colors of the two gel pens are identical so human vision is not able to distinguish the difference. The erased number is barely visible to human vision too. Next, we captured an image while the sample paper surface was illuminated with a broadband UV light source. The obtained image is shown in Fig. 5(b). The image shows an indistinct but perceptible number “0”, which is consistent with ultraviolet-fluorescent light [16]. This widely-adopted approach is able to identify the erased “0” but unable to identify that the number “1” was originally written by pen#1 but covered by pen#2.
Fig. 5 Color CCD camera measurement results of the forged handwriting. (a) Image illuminated with a white LED. (b) Image illuminated with a broadband UV light source.
4.3 Experiment results of UV enhanced CCD camera and narrowband UV light source
Secondly, the handwriting is analyzed by a UV enhanced CCD camera (FLI PL4710, MultiPix Imaging, UK) and two narrowband (10nm FWHM) UV LEDs. The central wavelength of the two LEDs are 278.5nm (LED#1) and 375.7nm (LED#2), measured by HR4000 Spectrometer (Ocean Optics, USA). We captured image of the sample under one narrowband UV LED illumination once. The obtained images are shown in Fig. 6(a) and Fig. 6(b) respectively. It is apparent that when illuminated with LED#1, the erased “0” is more visible than LED#2 illuminating condition. It results from the fact that the thermochromic ink is not actually removed from paper surface, but changes to white line when temperature rises above a certain temperature [18]. It shows that the erased ink of pen#1 contains substances with low reflectivity at 278.5nm and high reflectivity at 375.7nm. This approach is also widely-used and shows better results than the first approach in recovering the erased handwriting [17], but still not sufficient to identify that the number “1” was originally written by pen#1 but covered by pen#2.
Fig. 6 UV enhanced camera measurement results of the forged handwriting. (a) Image illuminated with LED#1. (b) Image illuminated with LED#2.
4.4 Experiment results of the imaging spectrometer and broadband UV light source
Thirdly, we captured the interferogram datacube of the sample paper surface. To accomplish HSI process, each interferogram image should be acquired with an exposure time of 1s and with an image of 300 × 230 pixels. In Section 2.1, we mention that the half of interferogram dimension is N = 512 pixels, which achieve the maximum spectral resolution. However, long measurement time is needed in this case since each column of the sample image is required to occupy each possible position over the wedge once. In practice, we could make each column of the sample image only scan a portion of the wedge. This operation reduces the measurement time at the cost of lower spectral resolution. Here, we reduce the half of interferogram dimension N to 128 and the acquisition time to about 10 minutes. Then the obtained data set is reconstructed into an interferogram datacube and is transformed into spectrum datacube with the Fourier transformation. The calibration result of Section 3 is used to further obtain the actual wavelength of the spectrum datacube. Following the same procedure given in Section 2.1, only 28 wavelength samples are left in the spectrum dimension. Thus, the final spectrum datacube has a dimension of 300 × 230 × 28.
Here, we are able to extract the images of the sample paper surface at selected UV wavelengths, such as 276.9nm, 297.4nm, 327.8nm or 356.9nm, as shown in Fig. 7 . It is apparent that the reflectivity of substances in erased ink of pen#1 has a prominent variation in near and middle UV band.
Fig. 7 Images of selected wavelengths extract from the spectrum datacube. (a) Image at 276.9nm. (b) Image at 297.4nm. (c) Image at 327.8nm. (d) Image at 356.9nm.
Since the spectrum datacube contains spectral information of each pixel with many wavelength samples, pattern recognition algorithm can be adopted to further analyze the data. In this work, we use the k-Means algorithm of Matlab. The spectrum of each pixel is considered as an observation, which is a 28-dimensional vector. We further normalized this vector by the sum of all the elements. This energy-normalized approach is to eliminate the effect of different reflectivity of the materials and uneven illumination intensity. The algorithm is able to partition all the observations (or all the pixels) into n sets so that the sum of distance functions of each point in the cluster to the n centers is minimal. The distance in this data space is defined as the squared Euclidean distance between the two observations.
Assuming three cluster centers, which are corresponding to the ink of pen#1, the ink of pen#2, and the white printing paper, the clustering result is illustrated in Fig. 8 . The pixels of each cluster are given a different color. The red color pixels belong to the erased number written by pen#1; while the blue color pixels belong to the numbers written by pen#2. Compared with the RGB color image in Fig. 5(a), it is apparent that the number “0” is erased. So far the approach gives no more information than the other approach.
However, the pixels at “|” stroke of number “4” shows blue and red colors. The red color pixels in this region indicate that the stroke was originally written by pen#1 too. So the original handwriting is actually “10”. On the other hand, it can be deduced that the stroke is covered by the ink of pen#2 since blue color pixels also exist, which is the same as the rest stroke of number “4”. Figure 9 shows the normalized reflective spectra of each pen ink and the white printing paper. The three normalized curves are the cluster centers. The absolute reflective spectra of paper are actually stronger than those of inks. Although the normalized curves are similar, the characteristic differences among the ink spectra and the paper spectra are still apparent.
Fig. 9 Normalized reflective spectra of the ink of pen#1, the ink of pen#2, and the white printing paper.
This experiment shows that the proposed imaging spectrometer is capable of capturing spectral data on the target surface with high spatial resolution and reasonably good spectral resolution. In practice, approximately 100 wavelength samples can be obtained in spectrum dimension so that more subtle difference in the spectra of different materials can be discovered. Such data is valuable for the applications of latent image analysis.
5. Conclusion
We have experimentally demonstrated a high resolution close-range ultraviolet imaging spectrometer. The wedge-shaped interferometric configuration conforms to the imaging condition which combines spatial and interference information into a high spatial resolution image. The spectrum datacube contains approximately 100 effective wavelength samples which cover both near and middle UV band. It is suitable for nondestructive analysis of thermochromic ink substance. A test run of the proposed system captured a datacube of a forged handwriting. The obtained spectrum datacube was analyzed by the k-Means algorithm. The results show that the original handwriting can be identified even if its strokes are either erased or covered by a different pen. The test demonstrates the potential of this proposed instrument. In the future, we plan to promote the spectral resolution and widen the scope of the working spectrum for the proposed imaging spectrometer. More advanced mathematical tools can also be introduced for the data mining of the spectrum datacube.
Acknowledgments
This work was performed under the auspices of the National Science & Technology Pillar Program (2012BAK02B04), Ministry of Public Security Key Research Foundation Project (2010ZDYJBJLG006), National Natural Science Foundation of China (60975013, 61575020), and Science and Technology Planning Project of Guangdong Province, China (2015A020214004).
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