Recovery of reflection spectra in a multispectral imaging system with

Recovery of reflection spectra in a multispectral imaging system with light emitting diodes Laure Fauch,* Ervin Nippolainen, Victor Teplov, and Alexei A. Kamshilin Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 1627, FIN-70211 Kuopio, Finland *[email protected]

Abstract: Performance of recently proposed multispectral imaging system for fast acquisition of two dimensional distribution of reflectance spectrum is experimentally studied. The system operation is based on a subspace vector model in which any reflectance spectrum is described in the compressed form as a linear combination of few spectral functions. A key element of the proposed system is a light source which includes a set of light-emitting diodes with different central wavelengths. The light source provides illumination of the object by fast-switchable sequences of spectral bands whose energy distributions are proportional to mutually orthogonal spectral functions (calculated in-advance). Object illumination is synchronized with a monochrome digital camera. The system allows us fast acquisition of reflectance spectra in a compressed form with high spatial resolution. A model of the system calibration by using standard white matte sample is proposed. Reconstruction of the reflectance spectrum from the compressed data collected after illumination of selected color samples from the Munsell book by 7 mutually orthogonal spectral functions is demonstrated. Parameters of the system, which affect the accuracy of the spectrum reconstruction, are analyzed and discussed. ©2010 Optical Society of America OCIS codes: (110.4234) Multispectral and hyperspectral imaging; (110.0110) Imaging system; (120.4820) Optical systems; (300.6550) Spectroscopy visible.

References and links M. B. Bouchard, B. R. Chen, S. A. Burgess, and E. M. C. Hillman, “Ultra-fast multispectral optical imaging of cortical oxygenation, blood flow, and intracellular calcium dynamics,” Opt. Express 17(18), 15670–15678 (2009). 2. A. K. Dunn, A. Devor, H. Bolay, M. L. Andermann, M. A. Moskowitz, A. M. Dale, and D. A. Boas, “Simultaneous imaging of total cerebral hemoglobin concentration, oxygenation, and blood flow during functional activation,” Opt. Lett. 28(1), 28–30 (2003). 3. S. A. Sheth, N. Prakash, M. Guiou, and A. W. Toga, “Validation and visualization of two-dimensional optical spectroscopic imaging of cerebral hemodynamics,” Neuroimage 47(Suppl 2), T36–T43 (2009). 4. D. Roblyer, R. Richards-Kortum, K. Sokolov, A. K. El-Naggar, M. D. Williams, C. Kurachi, and A. M. Gillenwater, “Multispectral optical imaging device for in vivo detection of oral neoplasia,” J. Biomed. Opt. 13(2), 024019 (2008). 5. V. C. Paquit, K. W. Tobin, J. R. Price, and F. Mèriaudeau, “3D and multispectral imaging for subcutaneous veins detection,” Opt. Express 17(14), 11360–11365 (2009). 6. A. Basiri, M. Nabili, S. Mathews, A. Libin, S. Groah, H. J. Noordmans, and J. C. Ramella-Roman, “Use of a multi-spectral camera in the characterization of skin wounds,” Opt. Express 18(4), 3244–3257 (2010). 7. L. Kong, D. Yi, S. Sprigle, F. Wang, C. Wang, F. Liu, A. Adibi, and R. Tummala, “Single sensor that outputs narrowband multispectral images,” J. Biomed. Opt. 15(1), 010502 (2010). 8. S. C. Gebhart, R. C. Thompson, and A. Mahadevan-Jansen, “Liquid-crystal tunable filter spectral imaging for brain tumor demarcation,” Appl. Opt. 46(10), 1896–1910 (2007). 9. E. M. Attas, M. G. Sowa, T. B. Posthumus, B. J. Schattka, H. H. Mantsch, and S. L. Zhang, “Near-IR spectroscopic imaging for skin hydration: the long and the short of it,” Biopolymers 67(2), 96–106 (2002). 10. J. Blasco, N. Aleixos, J. Gómez, and E. Moltó, “Citrus sorting by identification of the most common defects using multispectral computer vision,” J. Food Eng. 83(3), 384–393 (2007). 11. R. Lu, and Y. Peng, “Development of a multispectral imaging prototype for real-time detection of apple fruit firmness,” Opt. Eng. 46(12), 123201 (2007). 1.

#133484 - $15.00 USD

(C) 2010 OSA

Received 16 Aug 2010; revised 8 Oct 2010; accepted 11 Oct 2010; published 21 Oct 2010

25 October 2010 / Vol. 18, No. 22 / OPTICS EXPRESS 23394

12. J. Qiao, M. O. Ngadi, N. Wang, C. Gariépy, and S. O. Prasher, “Pork quality and marbling level assessment using a hyperspectral imaging system,” J. Food Eng. 83(1), 10–16 (2007). 13. A. A. Gowen, M. Taghizadeh, and C. P. O'Donnell, “Identification of mushrooms subjected to freeze damage using hyperspectral imaging,” J. Food Eng. 93(1), 7–12 (2009). 14. R. Leitner, H. Mairer, and A. Kercek, “Real-time classification of polymers with NIR spectral imaging and blob analysis,” Real-Time Imag. 9(4), 245–251 (2003). 15. P. B. García-Allende, O. M. Conde, A. M. Cubillas, C. Jáuregui, and J. M. López-Higuera, “New raw material discrimination system based on a spatial optical spectroscopy technique,” Sens. Actuators, A 135, 605–612 (2007). 16. P. Tatzer, M. Wolf, and T. Panner, “Industrial application for inline material sorting using hyperspectral imaging in the NIR range,” Real-Time Imag. 11(2), 99–107 (2005). 17. C. Bonifazzi, P. Carcagni, R. Fontana, M. Greco, M. Mastroiani, M. Materazzi, E. Pampaloni, L. Pezzati, and D. Bencini, “A scanning device for VIS–NIR multispectral imaging of paintings,” J. Opt. A, Pure Appl. Opt. 10(6), 064011 (2008). 18. D. Comelli, G. Valentini, A. Nevin, A. Farina, L. Toniolo, and R. Cubeddu, “A portable UV-fluorescence multispectral imaging system for the analysis of painted surfaces,” Rev. Sci. Instrum. 79(8), 086112 (2008). 19. L. Gao, R. T. Kester, N. Hagen, and T. S. Tkaczyk, “Snapshot Image Mapping Spectrometer (IMS) with high sampling density for hyperspectral microscopy,” Opt. Express 18(14), 14330–14344 (2010). 20. A. A. Kamshilin, and E. Nippolainen, “Chromatic discrimination by use of computer controlled set of lightemitting diodes,” Opt. Express 15(23), 15093–15100 (2007). 21. L. Fauch, E. Nippolainen, A. A. Kamshilin, M. Hauta-Kasari, J. P. S. Parkkinen, and T. Jaaskelainen, “Optical implementation of precise color classification using computer controlled set of light emitting diodes,” Opt. Rev. 14(4), 243–245 (2007). 22. E. Nippolainen, T. Ervasti, L. Fauch, S. V. Miridonov, J. Ketolainen, and A. A. Kamshilin, “Fast noncontact measurements of tablet dye concentration,” Opt. Express 18(15), 15624–15634 (2010). 23. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964). 24. L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3(10), 1673–1683 (1986). 25. J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6(2), 318–322 (1989). 26. T. Jaaskelainen, J. P. S. Parkkinen, and S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7(4), 725–730 (1990). 27. N. Hayasaka, S. Toyooka, and T. Jaaskelainen, “Iterative feedback method to make a spatial filter on a liquid crystal spatial light modulator for 2D spectroscopic pattern recognition,” Opt. Commun. 119(5-6), 643–651 (1995). 28. R. Piché, “Nonnegative color spectrum analysis filters from principal component analysis characteristic spectra,” J. Opt. Soc. Am. A 19(10), 1946–1950 (2002).

1. Introduction Development of multispectral imaging (MSI) systems attracts a lot of attention among researchers because these systems have great potential for application in numerous areas of science and technology. For example, complicated physiological and biological processes can be revealed and monitored while measuring spatial-temporal changes of reflected light simultaneously at several spectral bands [1–3]. In medicine, MSI system is used for early diagnosis of oral cancer [4], for subcutaneous veins detection [5], for monitoring of skinwounds healing [6,7], for spectral imaging of in vivo human cortex [8], and as a means to measure the degree of hydration of human skin in vivo [9]. In the food industry, MSI is applied to the detection of the quality of fruits [10,11], meat [12], and other food products [13]. Devices capable to acquire and analyze multispectral images are essential part of the online systems for quality control and/or discrimination of various products [14–16]. MSI systems are also used to support the diagnostics, conservation, and restoration of paintings and other artworks [17,18]. The most of these applications require that multispectral images are captured with high rate. Different types of MSI systems have been proposed aiming to achieve an optimal combination of the operation speed, spectral, and spatial resolutions. Note that the optimum is different for different applications. The first type of MSI systems incorporates a convenient single-point spectrometer and a 2D-scanning system [17]. It possesses good spectral and spatial resolution but requires long time to collect the data. The second type comprises a line-

#133484 - $15.00 USD

(C) 2010 OSA



scan spectrograph connected with a digital camera [12–16]. One frame of the camera contains the spectrum of the light reflected back from a line at the object surface. Very high spectral and spatial resolutions are achieved in this type of MSI systems. However, additional scanning perpendicular to the imaging line and significant compression of the data is needed in these systems. The third type of MSI system is a monochrome camera in combination with a filter wheel [2–4]. The spectral bands are switched mechanically and sequentially, which imposes serious constraints on both spectral resolution and operation speed. For simultaneous acquisition of images at several spectral bands, a lenslet array in which each lens is interfaced with narrowband filter was proposed instead of the filter wheel [6]. The same idea of simultaneous multispectral data acquisition was applied in [7] where a filter mosaic integrated with a CMOS imaging sensor was used instead of lenslet array. The operational speed of these systems is higher since it is defined solely by the frame rate of the digital camera at the expense of lower spatial and spectral resolution. Recent technological progress in development of liquid-crystal tunable filters (LCTF) made popular MSI systems in which a digital camera is combined with LCTF [8,9,18]. These systems are characterized by very high spectral and spatial resolution but inherent sequential mode of the spectral-bands switching limits the speed of data acquisition. Fast data acquisition of multispectral images is achieved in snapshot image mapping spectrometers [19] but these systems are expensive and require very large detector array. Recently new approach for design of MSI system was proposed in which the object under study is actively illuminated by light-emitting diodes (LEDs) generating different spectral bands [1,20,21] while the reflected light is captured by a monochrome camera synchronized with LED switching. The broad range of LEDs available today means that spectrally bright light sources can be obtained at almost any wavelength. Increase of the reflected light power together with ease of LED synchronization with a digital camera allows for acquisition of images at a very high frame rate. In the first version of such systems [1,20], object illumination by LEDs with different spectra bands was executed sequentially, which requires a large number of frames to be recorded in the case of increased spectral resolution. Recently we reported about design of modified MSI system in which an object is illuminated simultaneously by all LEDs covering wide spectral range (400 – 700 nm) [21]. A peculiar feature of this system is that it allows for acquisition of two-dimensional spatial distribution of the reflection spectra in the compressed form due to the illumination of the object by properly designed mutually orthogonal spectral functions. Therefore, the processing of the acquired data can be performed much faster and in a simpler way. In addition, such kind of MSI systems is not limited in the choice of the spectral bandwidth and can be easily extended to infrared or ultraviolet regions. In our previous articles [20–22], we showed that this system is capable of distinguishing samples with small differences in reflectance spectra, which was achieved by direct use of vector components representing compressed spectral data (without any reconstruction of reflectance spectra). In this article, we describe a calibration model and process of recovering the reflectance spectra from the image data obtained after illumination of a sample by 7 orthogonal spectral functions. Experiments were carried out with different color samples from the Munsell book. Illuminating spectral functions were implemented by means of a computercontrolled light source contained 17 LEDs. Parameters of the system, which affect the accuracy of these spectra reconstruction, have been analyzed. 2. System design 2.1. Principle of system operation In our method the object is illuminated by a computer-controlled light source which generates fast-switchable predefined sequences of spectral bands whose energy distribution is proportional to mutually orthogonal spectral functions [20]. During illumination by each

#133484 - $15.00 USD

(C) 2010 OSA



spectral function, the object image was captured by a monochrome CMOS-camera in a single frame. This approach is applicable for objects possessing smooth reflectance spectra which can be approximated by a linear combination of just a few spectral functions Si(λ) [23,24]: M

R( )    i Si   ,

(1)

i 1

where λ is the wavelength of light, the weighting coefficients σi are real numbers which unambiguously represent a particular reflectance spectrum within a given set of samples, M is the total number of spectral functions, and i is their sequential number. It was shown previously that surface-spectral reflectance in the visible spectral range of both natural and artificial objects can be quite satisfactory represented with the use 6 – 8 spectral functions [25,26].

Fig. 1. Seven mutually orthogonal spectral functions Si(λ) calculated in Ref [25]. from the measured reflectance spectra for color samples from the Munsell book.

Determination of these spectral functions is typically performed by using statistical analysis of the measured set of the reflectance spectra, for example, by principal component analysis of measured spectra of the given set of samples [25]. It should be pointed out that this approach works well only for objects which possess rather smooth reflectance spectra. In our experiment, we use 7 spectral functions calculated for optimal reconstruction of the spectral reflections of 1257 Munsell chips within the wavelengths range of 400-700 nm, which were published by Parkkinen et.al [25]. These spectral functions are shown in Fig. 1. As one can see, the most of these functions take both positive and negative values. However, the light energy is always positive. Therefore, straightforward design of light source with spectral distribution of the energy proportional to a spectral function is hardly possible. In our system, we take two measurements for each bipolar spectral function: during the first frame the object was illuminated by light with the spectrum from the positive part of the spectral function, while during the second frame the light spectrum was switched to only negative part of the same spectral function. The object response for complete bipolar spectral function is calculated digitally by subtraction of the second frame from the first one. Each pixel in the image after subtraction of these frames represents the weighting coefficient σi which corresponds to the particular spectral function Si(λ) [20]. After sequential illumination of the object by 7 spectral functions Si(λ) and calculation of difference between responses on positive and negative parts of these function we get 7 images from 13 captured frames (the

#133484 - $15.00 USD

(C) 2010 OSA



spectral function S1(λ) is always positive but others are bipolar). Two-dimensional distribution of the reflectance spectra is straightforward reconstructed from these 7 images by using Eq. (1). 2.2. Synthesis of spectral functions Experimental setup for acquisition of the compressed spectral function is rather simple as one can see in Fig. 2. A sample under study is illuminated by light emerged from a thick optical fiber (core diameter of 6 mm). Light reflected from the sample surface is captured by a CMOS digital camera. Therefore, the camera response after one frame is convolutions of the illuminating spectral function and the reflection coefficients of the sample, i.e. weighting coefficients σi [20]. The measured value of the coefficient σi primarily depends on the shape of the illuminating spectral function Si(λ). Our light source should generate sequences of spectral bands so that the spectral energy distribution during one frame is proportional to one of the spectral functions. The injection current and consequently the output optical power were kept unchangeable during the experiment. Therefore, for synthesis of the spectral function we modulate only duration of each LED emission. N

Si ( )   Dk    ti , k .

(2)

k

Here N is the total number of spectral bands (for our light source N = 17), Dk(λ) is the emission spectrum of each LED with k number (k = 1 to 17), and Δti,k is the set of the emission duration of the LEDs for implementation of the spectral function number i.

Fig. 2. Principle scheme of the system for fast acqusition of 2D distribution of the reflectance spectra.

Calculation of the exposure time Δti,k of each LED was done taking into account the spectral shape of LED emission, its output power, and spectral sensitivity of the CMOS camera because all these parameters affect the implementation of spectral functions. Before calculations we measured the output power and spectral bandwidth of each LED and spectral sensitivity of the used camera. Details of the experimental measurements and obtained results are reported in the following sections. The response of CMOS camera is proportional to the optical energy collected during one frame. However, the coefficient of proportionality, Csk, depends on the wavelength of the collected light. It was experimentally measured for each of 17 LEDs. The peak power density

#133484 - $15.00 USD

(C) 2010 OSA



pk, the central wavelength λk, and the spectral shape are different for different LEDs. Moreover, the spectral bands of LEDs with adjacent central wavelengths are overlapped, which is considered when we calculate the camera response, Rc(λ): N

Rc( )  RN   Dk    Csk    tk .

(3)

k

Here RN is the camera noise which is estimated as average response of the camera when all LEDs are switched off, and Δtk is duration of the emission of LED number k within one grabbed frame of CMOS camera. Our goal is illumination of the object by light whose spectrum is proportional to the spectral function Si(λ) in meaning that we estimate the effect by measuring the response of the digital camera. Therefore, a synthesized spectral function is written as N

Ssi ( )  Ai  Dk    Csk    ti , k ,

(4)

k

where Δti,k is the set of the emission duration of the 17 used LEDs for implementation of the spectral function number i, and Ai is the coefficient of proportionality. In this equation Dk(λ) and Csk(λ) are known, Ssi(λ) should be as close to Si(λ) as possible, while Ai and Δti,k are to be found. Procedure of evaluation procedure of both Ai and Δti,k is presented in Sect. 3 after description of the experimental setup. 2.3. Computer controlled light source For synthesis and synchronous fast switching of the spectral functions Si(λ) we use a computer controlled light source which is schematically shown in Fig. 2. It consists of 17 LEDs with different central wavelengths of emission, which cover the wavelength range from 400 to 700 nm. Each LED is coupled to an optical fiber of small core diameter (950 µm). The light emerged from each fiber is mixed inside thick optical fiber with the core diameter of 6000 µm, which results in rather uniform spatial distribution of the output intensity at the object surface. The moments of switching on/off are controlled by the computer separately for each LED by means of custom-designed electronic controller. The spectral power distribution of the LEDs used is shown in Fig. 3 as it was measured at the output of the thick fiber. The measurements of LED parameters were carried out using a spectrograph (model SR-3031 of Andor Co.) and a conventional power-meter. As seen in Fig. 3, both the output power and bandwidth of our spectral bands are varying from one LED to another. The parameters λk, pk, and the spectral shape obtained from these measurements were used for calculation of the emission time Δti,k needed to implement the spectral functions. During fabrication of the light source we took special care for coupling of 17 thin fibers with the thick fiber. The goal was to achieve the best possible overlapping of the illuminated area at the object surface by the light emitted from all the LEDs. After such an adjustment all the fibers were glued. The length of the thick fiber was 1 m which allows achievement of satisfactory mixture of the luminous flux from all 17 LEDs. The end of the thick fiber was placed at the distance of 12 mm from the object. The diameter of the light spot on the object surface was about 27 mm. Typical photograph of the spot at the object is shown in Fig. 4. The illumination angle provided by the light emerged from the thick fiber was 45°  20° due to beam divergence. This photograph was taken under illumination of the standard matte white sample by the light of LED with λκ = 472 nm. Other LEDs provide almost the same shape of the illuminating spot. In our prototype of the light source about 90% of the area of illuminating spots was common for all 17 LEDs.

#133484 - $15.00 USD

(C) 2010 OSA



Fig. 3. Spectral power distribution of 17 LEDs used in our light source.

Fig. 4. Typical image captured by CMOS camera (white color corresponds to high irradiance) under illumination by the LED with central wavelength of 472 nm. Red circle shows the region in which the MSI system calibration and measurements of the reflection spectra were carried out.

2.4. Spectral sensitivity of the CMOS camera Light reflected from the object is collected into a monochrome CMOS camera (model EO1312 of the Edmund Optics Inc.) by means of conventional C-mount lens so that to form the focused image of the object surface. The camera was set so that the axis of its lens coincides with the normal to the sample surface. These conditions of the illumination and observation were identical to those at which the reflectance spectra of color samples of the Munsell book were measured. The distance between the object surface and an outer surface of the camera lens was 58 mm. The dynamic range of our digital camera is 8 bits. Raw images were recorded into a personal computer in the bitmap format. The camera provides capturing of the images with size of 1024 × 1280 pixels. As one can see in Fig. 4, the size of the illuminated spot at the image was smaller than the region imaged onto the detector array. All measurements were carried out within even smaller window which contains 7825 pixels (marked by a red circle in Fig. 4) to be sure that the intensity of the illuminating light is uniform inside this window. Responses of all pixels within the measuring window were spatially averaged. The frame rate of the camera was set to 2 fps. Dependence of the camera response on the light exposure was measured when it was illuminated by each of 17 LEDs varying the emission time from 5 to 150 ms. The results are shown in Fig. 5a for two LEDs with the central wavelength of 442 and 638 nm, as an example. One can see that the camera response linearly depends on the energy of the collected light when it does not exceed the level of 150. Saturation of the camera response is observed at higher magnitude. Sensitivity of the camera, Csk(λ), is defined as the gradient of

#133484 - $15.00 USD

(C) 2010 OSA



the curves shown in Fig. 5a. Sensitivity Csk strongly depends on the wavelength as it is shown in Fig. 5b. These data were used for calculating the exposure times Δti,k.

Fig. 5. Camera response as a function of the light exposure for two LEDs at the wavelength of 442 nm (squares) and 638 nm (circles) (a); Spectral dependence of the camera sensitivity (b).

3. System calibration 3.1. Calculating duration of LEDs emission Calibration of the MSI system was carried out using a standard matte white sample (B97) with known reflectance spectrum. The sample was illuminated under the angle of 45° while the reflected light was collected into the digital camera at 0° (see Sect. 2.4). These conditions of the sample illumination and reflection observation were the same as during the measurements of its reflectance spectrum Rw(λ) by the conventional method. The emission spectrum Dk(λ) of each LED is measured in the units of power emerged from the thick fiber. However, amount of the diffusely reflected light from the object is proportional to the intensity of illuminating light, not to its power. Both the divergence and angle of the illumination may slightly vary from one LED to another even in the case when all light is emerged from the same fiber. We benefit from the flat spectral dependence of the white standard sample to find actual ratios of the light intensity between different LEDs for the selected area of the object corresponding to the mask of its image. These intensity ratios were used for calculations of sets of Δti,k. Under illumination of the sample by the theoretically calculated spectral function Si(λ) the expected response is the weighting coefficient σi:

 i   Rw    Si    d .

(5)

To find the parameters Ai and Δti,k we simulate the response of the camera (denoted by σsi) on the illumination of the standard white sample by the i-spectral function as: 

N





k



 si  Ai  Rw      Dk    Csk    ti ,k  d .

(6)

The least square method was used to find the exposure times Δti,k from the condition that the shape of the synthesized spectral functions given by Eq. (4) is as close to the theoretically calculated spectral functions as possible. The coefficients Ai are found from the condition  i   si . Figure 6 shows the results of the synthesis of spectral functions S1(λ) and S2(λ).The other 5 functions are not shown but have similar behavior.

#133484 - $15.00 USD

(C) 2010 OSA



Fig. 6. The first (a) and second (b) spectral functions S1(λ) and S2(λ) as calculated theoretically (blue lines) and their implementation by the available 17 LEDs (red lines).

As one can see, the limited number of spectral bands provided by used LEDs does not allow us to synthesize the spectral functions with high accuracy but their main peculiarities are reasonably reproduced. 3.2. Reflectance spectrum reconstruction of the white standard After calculation of the exposure time Δti,k for all 17 LEDs to implement 7 spectral functions, these data were uploaded into the electronic controller which is synchronized with the digital camera. During one frame of the camera all the LEDs needed to implement the positive (or negative) part of the spectra are switched on and then switched off according to the uploaded program. During the next frame, another set of the exposure times is executed thus implementing another part of the spectral function. 13 frames are needed for the sample illumination by the complete set of the spectral functions. After subtracting the camera responses on the positive and negative parts of the spectral functions we get 7 weighting coefficients σei. At the stage of the spectrum reconstruction we just multiply the measured weighting coefficient by the respective spectral function: M

RE ( )    ei Si   .

(7)

i 1

The result of the spectrum reconstruction is shown in Fig. 7 by the red solid line. The original spectrum is shown by the solid black line. Dashed blue line shows the theoretical reconstruction of the same spectrum by calculating the weighting coefficients as a dot product of each spectral function with original reflectance spectrum. One can see that the reconstructed spectrum deviates from the original spectrum by less than 10%. This is a good result for the first attempt of the experimental verification of novel approach of 2D reflectance spectrum measurements by illuminating the object with mutually orthogonal spectral functions.

#133484 - $15.00 USD

(C) 2010 OSA



Fig. 7. Reflectance spectrum of the standard matte white sample (black). The spectrum reconstructed using Eq. (7) with the measured coefficients σei is shown by the red solid line. Dashed blue line snows for comparison the spectrum reconstructed using Eq. (1) with theoretically calculated weighting coefficients σi.

4. Results for spectra reconstruction of color samples and discussion Three color samples from the Munsell book were used to check feasibility of our MSI system for measurement and reconstruction the reflectance spectra. These samples are: 5R7/8 (red), 5Y7/8 (yellow), and 5B7/8 (blue). Their reflectance spectra were preliminary measured by the spectrometer under illumination by a D-65 light source. These samples were chosen so that the maxima of their reflectance spectra are situated at different regions of the visible range of the spectrum. The experimental conditions of the measurements with our MSI system were the same as for the system calibration with the white matte standard sample (see previous Sect.3). The reconstruction of the reflectance spectra was done in the similar way as it is described in Sect.3.2. The results are shown in Fig. 8 where the original spectra are given by black solid lines and the reconstructed spectra are given by colored lines with dots. Spectra of the red, yellow, and blue samples are shown in Fig. 8 a, b, and c, respectively. As one can see the measured samples can be easily recognized. The red sample possesses the maximum of its reflectance spectra in the red region of the visible spectral range, which is the same for its original spectrum and for the reconstructed one from the measured coefficients σei. The yellow sample should present a reflectance spectrum with a maximum in the middle of the visible spectral range (at about 550 nm) which is the case for both reconstructed and original reflectance spectra. The blue sample should have the maximum of reflectance in the blue-green region (about 500 nm). As one can see in Fig. 8 the maxima of both curves are achieved at almost the same wavelength. However, there is easy visible discrepancy between the original and reconstructed spectra which does not exceed 10%. We believe that the reason of this discrepancy is the same as for the reconstructed spectrum of the white standard: not exact implementation of spectral functions by the available set of LEDs. Nevertheless, the reconstructed spectra are rather closed to their original, which shows that our approach allows reconstructing the reflectance spectra in the wide wavelength range from 400 nm to 700 nm. In the proposed MSI system closeness of the synthesized spectral functions Ssi(λ) to the calculated in advance functions Si(λ) primarily defines accuracy of the reflectance spectra reconstruction. In its turn it is the set of Δti,k which defines the shape and the magnitude of the synthesized spectral functions. These parameters Δti,k are defined by the relative intensity of the object illumination provided by different LEDs. During the calibration procedure we choose the mask corresponding to a certain area at the object surface within which the relative intensities of the object illumination are measured. Parameters Δti,k are calculated for the particular ratios of intensities within the chosen object area. If the illumination-intensities

#133484 - $15.00 USD

(C) 2010 OSA



ratios in another object area are seriously different from that of the chosen area, the reflectance spectrum will be incorrectly reconstructed. Unfortunately in our first version of a home-made light source, these intensities ratios are functions of both the position of the chosen mask and the distance between the object and illuminating fiber-end. It means that the object under study should be situated exactly in the place of the white standard used for the system calibration.

Fig. 8. Reflectance spectra of 3 color chips from the Munsell book: (a) red 5R7/8; (b) yellow 5Y7/8; and (c) blue 5B7/8. Spectra reconstructed from the measurements with our MSI system are shown by colored solid lines with dots; black solid lines represent conventionally measured spectra.

Therefore, for correct reconstruction of the reflectance spectra from the sample, the ideal light source should provide uniform illumination of the whole area of the sample under the same angle of incidence for all used LEDs. In our light source uniformity of the illumination was not very high but it allows us to recognize the problem. The technology of the light source fabrication should be improved for recovery of reflectance spectrum distribution from a large sample area. It should be noted that measurements of relative changes of the reflection spectra distribution (or its dynamics) can be carried out without spectra reconstructions. The relative change of the weighting coefficients can be measured without system calibration and even in the case when spectral functions are not correctly represented because the weighting coefficients completely represent the shape of the reflection spectrum (see Eq. (1). This was a reason of successful distinguishing of samples with small difference of reflection spectra achieved with the proposed approach in our previous articles [20,21]. To demonstrate feasibility of our MSI system for quantitative reconstruction of the reflectance spectra we use in this study 7 spectral functions which contain both positive and negative values. This set of functions requires applying of two illuminations for implementation of every function, with total of 13 illuminations, and respectively, frames

#133484 - $15.00 USD

(C) 2010 OSA



being required to acquire all necessary data. Nevertheless, in several research groups, some efforts were applied to search for approximate spectral functions with non-negative values that can accurately enough represent any spectral reflectance from the given set of objects surfaces [27,28]. Use of non-negative spectral functions certainly leads to reduced number of frames thus increasing the speed of operation of the MSI system. In the future work we are planning to test performance of the system with non-negative spectral functions. We also expect to improve quality of the spectra reconstruction by using a camera with higher dynamic range (12 – 14 bits) which increases the spectral range of the linear response of the camera. Higher range of linearity would result in better implementation of the spectral functions and therefore, in more accurate reflection spectra reconstruction. 5. Conclusion In this paper, we present experimental results of using recently proposed multispectral imaging system for quantitative reconstruction of two dimensional distributions of reflectance spectra with high spatial distribution. The key device of the system is a computer controlled light source which generates any fast-switching sequence of spectral distribution whose energy distribution is proportional to mutually orthogonal spectral functions calculated in advance. The reflection spectra are compressed at the stage of measurements inside few camera frames and these compressed data are used for spectra reconstruction. The calibration of the proposed system was carried out by using the standard matte white sample with known reflectance spectrum. Three different color samples from the Munsell book (red, yellow, and green-blue) were chosen for testing the system in its ability of measurements and reconstruction their reflection spectra. Results show that the shapes of the spectral curves are reconstructed correctly but their magnitudes deviate from the original spectra within 20%. This is a good result for the first attempt of the quantitative spectra reconstruction using novel approach of object illumination by the mutually orthogonal spectral functions. Nevertheless, our experiments show feasibility of the proposed approach. Our study has revealed that the light source should provide a uniform illumination of the object by every LED for correct reconstruction of the reflectance spectra from the whole illuminated area. We believe that new system of fast measurements of 2D distribution of reflection spectra can find wide range of applications. Acknowledgments The authors would like to acknowledge the Academy of Finland for partial financial support of the research (Project No. 128582).

#133484 - $15.00 USD

(C) 2010 OSA

