spectroscopic techniques

Single-Shot Digital Holography Using a Spectral Estimation Technique Peng Xia,a,b,* Yasuhiro Awatsuji,a Kenzo Nishio,c Shogo Ura,a Osamu Matobad a

Graduate School of Science and Technology, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan Research Fellow of the Japan Society for the Promotion of Science, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083, Japan c Advanced Technology Center, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan d Graduate School of System Informatics, Kobe University, Rokkodai 1-1, Nada-ku, Kobe 657-8501, Japan b

We demonstrate a technique capable of obtaining spectral information and a three-dimensional (3D) profile of an object with a single-shot exposure. This technique is based on digital holography and the spectral estimation technique. In the demonstration of this technique, we simultaneously use three laser lines operating at 473, 532, and 633 nm to record the multiple complex amplitudes of the object corresponding to the wavelengths and obtain reconstructed monochrome images of each wavelength. A spectral estimation technique is applied to estimate the spectral reflectance of the object from the reconstructed monochrome images. We experimentally succeed in estimating the spectral reflectance of a lemon by using the technique. Index Headings: Spectral imaging; Digital holography; Phase imaging; Three-dimensional imaging.

INTRODUCTION The spectroscopic measurement of an object is very useful in the fields of medicine, food safety inspection, cell analysis, and others. Up to now, many spectroscopic measurement methods have been proposed. Raman spectroscopy especially has been widely investigated in many fields.1–4 Raman spectroscopy shows a strong potential for providing information from various samples in a non-invasive way that is important in medicine and biology, and may be combined with confocal microscopy to obtain spectral information and the three-dimensional (3D) information of objects.5,6 However, in this technique, scanning an object is required to record 3D information, which is very time-consuming and is useless for a moving object. Holography7,8 is a useful technique for recording and reconstructing the perfect wave fronts of objects without scanning. In this technique, 3D information of an object is recorded in a hologram, consisting of media such as photographic plates or photorefractive crystals, and the Received 24 February 2014; accepted 7 May 2014. * Author to whom correspondence should be sent. E-mail: awatsuji@ kit.ac.jp. DOI: 10.1366/14-07504

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3D image of the object is reconstructed by illuminating the hologram with a laser or some other light beam. Recently, there has been a great deal of progress in image sensors, such as charge-coupled devices (CCDs) and complementary metal-oxide semiconductors (CMOSs), and such devices have been used in holography in place of conventional recording media. Holography that uses image sensors is called digital holography,9,10 which is a technique capable of 3D measurement and has been actively applied in many fields, such as microscopy,11–13 particle measurement,14 object recognition,15 3D imaging,16 and so on. In general, the light source used in digital holography is a coherent light source whose optical bandwidth is very narrow so that it is impossible to record the spectral information of an object. Multi-wavelength digital holography for 3D object visualization and recognition using two wavelengths based on the principal component analysis (PCA) technique and the mixture discriminant analysis (MDA) technique17 to provide spatial and spectral information of 3D objects was proposed. However, this technique only provides two images of two wavelengths. Subsequently, a fully passive interferometric technique capable of obtaining both 3D images and spectral information of spatially incoherent and polychromatic objects was investigated.18 However, the scanning of an object is required also, so that it is useless for a moving object. In some applications, any techniques which can obtain spectral reflectance information and 3D profile of objects in a shorter time are required urgently, such as living cell observation, fluid measurement, and so on. In multispectral imaging,19 a spectral estimation technique was reported, and we have applied the technique to color digital holography to improve the color reproduction of the reconstructed image.20,21 However, in the previous report on digital holography, multiple exposures were required to record the holograms of the object because phase-shifting interferometry22 was applied to the holography in order to separate the desired image, which was the first-order diffracted wave, from the undesired images, which were the zeroth-order diffracted wave and the minus-first

0003-7028/14/6811-1296/0 Q 2014 Society for Applied Spectroscopy

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diffracted wave. Consequently, it is useless for measuring a moving object. In this paper, we demonstrate a single-shot digital holography using the spectral estimation technique. By comparing our proposed method with the aforementioned methods, the 3D profile information of an object can be measured with a single-shot exposure without scanning the object, which enables the measurement of a high-speed moving object. Additionally, three laser lines operating at 473, 532, and 633 nm are used to record the multiple complex amplitudes of the object, and reconstructed monochrome images of these three laser lines are applied to estimate the spectral reflectance of the object by using the spectral estimation technique. Therefore, the proposed method enables the instantaneous acquisition of spectral information and the 3D profile information of a moving object. We also explain the principle of the proposed technique and apply the technique to estimate the spectral reflectance of a lemon, as an example of food inspection, to confirm the effectiveness of the technique.

METHODS Digital Holography. Digital holography is a technique used to record complex amplitude of an object via a CCD camera or a similar device and reconstruct the 3D images of the object by computer. The resultant intensity to be recorded by a CCD camera is expressed as Iðx ; y Þ ¼ jRðx ; y Þj2 þ jOðx ; y Þj2 þ O  ðx ; y ÞRðx ; y Þ þ Oðx ; y ÞR  ðx ; y Þ ð1Þ where R and O denote complex amplitude distributions of reference wave and object wave, respectively. Starred (*) symbols mean complex conjugate values. In Eq. 1, the terms (jR(x, y)j2 þ jO(x, y)j)2 and the term (O*(x, y)R(x, y)) and the term (O(x, y)R*(x, y)) are the zeroth-order diffracted wave, the minus-first diffracted wave, and the first-order diffracted wave, respectively. The first-order diffracted wave includes the complex amplitude distribution of the object wave that we want to obtain. According to the incident angle between the reference beam and the object beam, the recording method can be grouped in two main categories: inline23 and off-axis configurations.24 With in-line digital holography, the minus-first and the zeroth-order diffracted waves are superimposed on the first-order diffracted wave that forms the image of the object, which deteriorates the image quality. To solve this problem, phase-shifting digital holography was proposed.22 In this technique, four phase-shifted holograms are recorded to remove the minus-first and the zeroth-order diffracted waves to obtain a clear object image. For our applications, three reconstructed images of three laser lines are needed to estimate the spectral reflectance of the object. This means 12 holograms should be recorded. It is apparent that it is very difficult to record 12 holograms with single-shot exposure. So we employed off-axis digital holography to achieve our proposed technique. Off-Axis Digital Holography. Figure 1 shows an example of optical setup of off-axis digital holography

FIG. 1. One example of setup of off-axis digital holography.

for recording a monochrome 3D image of an object. A light beam is emitted from the laser and is split into two beams by a beam splitter. One beam passes through a microscope objective and illuminates the object. The scattered light from the object, called an object beam, is incident to the image sensor. The other beam, called a reference beam, passes through the other microscope objective and then arrives at the image sensor. The reference and object beams are incident to the image sensor with a relative angle. The hologram is an interferogram generated by the interference between the object wave, and the reference wave is recorded by the image sensor. When we reconstruct the object image from the recorded hologram, Fourier transform is applied to the recorded hologram. In the spatialfrequency domain, the spatial-frequency spectra of the zeroth-order diffracted wave, the minus-first diffracted wave, and the first-order diffracted wave are separated in the direction of the off-axis angle between the reference and object beams. For example, if the reference and object beams are incident to the image sensor with a relative angle in x-direction, as shown in Fig. 2, the spatial-frequency spectra of the zeroth-order diffracted wave, the minus-first diffracted wave, and the first-order diffracted wave will be separated in xdirection, as shown in Fig. 3, where the areas are indicated by circles. After that, the spectrum of the firstorder diffracted wave is extracted by spatial filtering. Finally, we apply inverse Fourier transform and diffrac-

FIG. 2. One example of recording of hologram when the reference and object beams are incident to the image sensor with a relative angle in the x-direction.

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FIG. 3. Schematic of the appearance of the spatial-frequency spectrum of the hologram that was recorded as shown in Fig. 2.

tion integral to the extracted spatial-frequency spectrum to obtain the object image. For our proposed technique, three reconstructed images corresponding to three laser lines are required. Likewise, through adjusting the incident angles between reference and object beams of these three laser lines in different directions, the spatial-frequency spectra of the zeroth-order diffracted wave, the minus-first diffracted wave, and the first-order diffracted wave of these three laser lines will be separated in the spatial-frequency domain, respectively. Figure 4 shows a schematic of the appearance of the spatial-frequency spectra of the hologram recorded by blue (B), green (G), and red (R) laser lines in off-axis digital holography. In the recorded hologram, the object beams of BGR are vertically incident to the image sensor in z-direction, and the reference beams of BGR are incident to the image sensor at relative angles in x, y, and between the x- and y-directions. The first-order diffracted waves of each laser line are extracted by spatial filtering. Finally, the 3D object images of each laser line can be obtained through the image processing that applies the calculations of inverse Fourier transform and diffraction integral to the extracted spatial-frequency spectra. Digital holography reconstructs the image of an object by computer and therefore has the following attractive features: a wet process for developing recording media is not required, quantitative evaluation is easy for 3D images of objects, and focused images of 3D objects at a desired depth can be instantaneously acquired without a mechanical focusing process. Digital Holography Using Spectral Estimation Technique. The spectral estimation technique can estimate the spectral reflectance of the object from multiple discrete reflectances. This technique is very valuable

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FIG. 4. Schematic of the appearance of the spatial-frequency spectrum of a hologram recorded by three laser lines. The subscripts r, g, and b mean red, green, and blue laser lines, respectively.

and has been applied to image diagnosis, such as endoscopy (for example, 500 Series made by Fujifilm company25). However, this technique only provides twodimensional images of an object. We introduced the spectral estimation technique to multiple wavelength digital holography26–28 to achieve a technique capable of obtaining both spectral information and a 3D profile of moving objects simultaneously. The principle of this technique is schematically shown in Fig. 5. First, multiple monochrome images are reconstructed by digital holography to obtain the intensity values of reconstructed images g (gR, gG, gB). After that, the estimating constant matrix A is calculated. Finally, the estimated reflectance of the object can be calculated from the intensity values of reconstructed images g and the estimating constant matrix A. The detailed calculations of the estimated reflectance of the object and the estimating constant matrix A are described below. The following process is performed on a pixel-by-pixel basis. To understand the principle of spectral estimation easily, we defined some parameters firstly. Here, k, r(k), I(k), and S(k) are wavelength, the spectral reflectance of the object, the spectral power distribution of the illuminant for recording of the hologram, and the spectral sensitivity of the image sensor, respectively. A pixel value of the image is calculated by using the following equation.

R

R

gi ¼ Sðki ÞIðki Þr ðkÞd k ¼ Hðki Þr ðkÞd k

ð2Þ

Here, i is the laser line (i = B, G, R, etc.), and H(ki) is equal to S(ki)I(ki). Then Eq. 2 can be written in vector and matrix notation as follows: g ¼ Hr

ð3Þ

FIG. 7.

FIG. 5. Principle of digital holography using the spectral estimation technique.

The spectral characteristics are set to m wavelengths. If the number of laser lines used for recording a hologram is set to n, g is the n 3 1 vector of the intensity value, H is the n 3 m matrix comprising the spectral power distribution of the illuminant and the spectral sensitivity of the image sensor, and r is the m 3 1 vector of the spectral reflectance of the object. Here, n is smaller than m in spectral analyses of an object because the number of the laser lines used for recording holograms is finite, in general. Then it is impossible to determine the unique solution of Eq. 3 for r when m . n. To estimate the spectral reflectance distribution of the object, whose spectral reflectance distribution has been unknown, from the three reconstructed intensity distributions, an estimating constant matrix A is introduced. The estimated spectral reflectance distribution rest can be calculated by using the following equation. rˆ est ¼ Ag

ð4Þ

Optical setup of the experiment.

between the original and the estimated spectral reflectance D E D E ð5Þ jjr  rˆ est jj2 ¼ jjr  Agjj2 ! min Here, left and right angle brackets (, .) and r denote ensemble average and spectral reflectances of samples, respectively. Here, A is calculated by using the following equation:29 A ¼ Cr Ht ðHCr Ht Þ1

ð6Þ

where t denotes transposition. Here, Cr is an m 3 m covariance matrix of the spectral reflectances of many samples and calculated by using the following equation: D E ð7Þ Cr ¼ ðr  rÞðr  rÞt Here, r¯ denotes the average spectral reflectance of many samples. Therefore, to estimate the spectral reflectance of the object, various samples should be prepared in advance. After that, the covariance matrix Cr is calculated. Then we can obtain the estimating constant

where the circumflex () denotes the estimator. Here, the estimating constant matrix A is determined such that it minimizes the ensemble average of the square error

FIG. 6. Photograph of the object.

FIG. 8. The recorded hologram.

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FIG. 10. Reconstructed images in the experiment. (a) red (633 nm), (b) green (532 nm), and (c) blue (473 nm).

RESULTS AND DISCUSSIONS

FIG. 9. Fourier transformed image of the recorded hologram.

matrix A. Finally, the estimating constant matrix A is used to estimate the spectral reflectance of the object.

EXPERIMENTAL As an example of a food inspection application, a lemon was used as the experimental object (Fig. 6). The lemon was located 34 cm apart from the image sensor plane. The measured area is marked by an open square, as shown in Fig. 6, and the size of the measured area is 1 3 1 cm. Figure 7 shows the optical setup of the experiment. This is an off-axis digital holography system that simultaneously uses three laser lines: a He-Ne laser operated at 633 nm, a neodymium-doped yttrium orthovanadate (Nd : YVO4) laser operated at 532 nm, and a neodymium-doped yttrium aluminum garnet (Nd : YAG) laser operated at 473 nm. Three laser lines, red, green and blue beams, were chosen to cover visible range widely. A monochrome CMOS camera with pixel size 1.67 3 1.67 lm was used to record the hologram. By adjusting the incident angles of these three laser lines, we recorded a hologram, as shown in Fig. 8, and the Fourier transformed image of it is shown in Fig. 9. We can see that the spatial-frequency spectra of the zerothorder diffracted wave, the minus-first diffracted wave, and the first-order diffracted wave of these three laser lines separately appeared in the spatial-frequency domain, which is almost the same as Fig. 4. After that, the spatial-domain spectrum of the object wave of each wavelength was extracted. Finally, we applied inverse Fourier transform and diffraction integral to each extracted spatial-domain spectrum to obtain the object image. By this method, object images of three laser lines were obtained from a single recorded hologram. The reconstructed images of each wavelength are shown in Fig. 10.

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The spectral power distribution of each illuminant I(k) was measured by an optical power meter, and the spectral sensitivities of the image sensor S(k) are given by the manufacturer. Spectral reflectances of 24 lemons were measured as samples by a spectrophotometer to calculate the covariance matrix Cr. The more the samples, the higher the precision. To make the experiment easy to perform, we chose 24 lemons as samples, which were enough to get the covariance matrix. The bands of the estimated spectral reflectance distribution of the object were set to 400–700 nm with a 5 nm step, and then the spectral characteristic m was 61. We used the R, G, and B monochrome images to estimate the spectral reflectance of the object and compared the results with values measured by the spectrophotometer. The result is shown in Fig. 11. We can see that the curve generated by the estimated spectral reflectance distributions in experiment greatly agreed with that generated by the values measured by the spectrophotometer, which confirmed the effectiveness of the technique. However, there exists some disagreement because only three laser lines were used to estimate the spectral reflectance distributions of the object. The number of the laser lines is not sufficient, and then the results in some bands were not completely satisfactory. Moreover, the adjustment of the optical setup may influence the estimated results. If the laser lines operating at other wavelengths were added to record holograms, the results of the estimated spectral distributions could be improved possibly. In addition, if an infrared laser or ultraviolet laser is introduced into this technique, it is

FIG. 11. Experiment result.

possible that the spectral reflectance distribution of an object in the infrared band or ultraviolet band is estimated. Additionally, the image compression and encryption are very important in digital holography for decreasing the size of the stored data for increasing the efficiency of telecommunication and enhancing the safety of the data.30,31

CONCLUSION In conclusion, we demonstrated single-shot digital holography using the spectral estimation technique being capable of obtaining spectral information and 3D images of a moving object. We succeeded in measuring the spectral reflectance of a lemon by using the technique, which confirmed the effectiveness of the technique. Through the spectral estimation technique, the spectral reflectance distribution of object can be obtained, which will contribute to high-precision 3D measurement and spectroscopic measurement of an object, such as blood measurement, living cell measurement, medical diagnosis, and so on. ACKNOWLEDGMENTS This study was partially supported by Grant-in-Aid for Japan Society for the Promotion of Science (JSPS) Fellows and by the Funding Program for Next Generation World-Leading Researchers GR064 of JSPS. 1. R.F. Begley, A.B. Harvey, R.L. Byer. ‘‘Coherent Anti-Stokes Raman Spectroscopy’’. Appl. Phys. Lett. 1974. 25(7): 387-390. 2. L.J. Goeller, M.R. Riley. ‘‘Discrimination of Bacteria and Bacteriophages by Raman Spectroscopy and Surface-Enhanced Raman Spectroscopy’’. Appl. Spectrosc. 2007. 61(7): 679-685. 3. S.O. Konorov, M.W. Blades, R.F.B. Turner. ‘‘Non-Resonant Background Suppression by Destructive Interference in Coherent AntiStokes Raman Scattering Spectroscopy’’. Opt. Express. 2011. 19(27): 25925-25934. 4. H.G. Schulze, R.F.B. Turner. ‘‘Two-Dimensionally Coincident Second Difference Cosmic Ray Spike Removal Method for the Fully Automated Processing of Raman Spectra’’. Appl. Spectrosc. 2014. 68(2): 185-191. 5. A. Govil, D.M. Pallister, M.D. Morris. ‘‘Three-Dimensional Digital Confocal Raman Microscopy’’. Appl. Spectrosc. 1993. 47(1): 75-79. 6. C.J.H. Brenan, I.W. Hunter. ‘‘Chemical Imaging with a Confocal Scanning Fourier-Transform-Raman Microscope’’. Appl. Opt. 1994. 33(31): 7520-7528. 7. D. Gabor. ‘‘A New Microscopic Principle’’. Nature. 1948. 161: 777778. 8. E.N. Leith, J. Upatnieks. ‘‘Wavefront Reconstruction with Diffused Illumination and Three-Dimensional Objects’’. J. Opt. Soc. Am. 1964. 54(11): 1295-1301. 9. J.W. Goodman, R.W. Lawrence. ‘‘Digital Image Formation from Electronically Detected Holograms’’. Appl. Phys. Lett. 1967. 11: 7779. 10. U. Schnars, W.P. Ju¨ptner. ‘‘Direct Recording of Holograms by a CCD Target and Numerical Reconstruction’’. Appl. Opt. 1994. 33(2): 179-181.

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Single-shot digital holography using a spectral estimation technique.

We demonstrate a technique capable of obtaining spectral information and a three-dimensional (3D) profile of an object with a single-shot exposure. Th...
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