Abstract

The spectral content of a sample provides important information that cannot be detected by the human eye or by using an ordinary RGB camera. The spectrum is typically a fingerprint of the chemical compound, its environmental conditions, phase and geometry. Thus measuring the spectrum at each point of a sample is important for a large range of applications from art preservation through forensics to pathological analysis of a tissue section. To date, however, there is no system that can measure the spectral image of a large sample in a reasonable time. Here we present a novel method for scanning very large spectral images of microscopy samples even if they cannot be viewed in a single field of view of the camera. The system is based on capturing information while the sample is being scanned continuously ‘on the fly’. Spectral separation implements Fourier spectroscopy by using an interferometer mounted along the optical axis. High spectral resolution of ~5 nm at 500 nm could be achieved with a diffraction-limited spatial resolution. The acquisition time is fairly high and takes 6-8 minutes for a sample size of 10mm x 10mm measured under a bright-field microscope using a 20X magnification.

© 2016 Optical Society of America

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References

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2013 (2)

F. Ghaznavi, A. Evans, A. Madabhushi, and M. Feldman, “Digital imaging in pathology: whole-slide imaging and beyond,” Annu. Rev. Pathol. 8(1), 331–359 (2013).
[Crossref] [PubMed]

W. Huang, K. Hennrick, and S. Drew, “A colorful future of quantitative pathology: validation of Vectra technology using chromogenic multiplexed immunohistochemistry and prostate tissue microarrays,” Hum. Pathol. 44(1), 29–38 (2013).
[Crossref] [PubMed]

2010 (4)

2009 (2)

2007 (1)

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3-5 μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[Crossref]

2006 (1)

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: principles and applications,” Cytometry A 69(8), 735–747 (2006).
[Crossref] [PubMed]

2005 (1)

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93(2), 216–231 (2005).
[Crossref]

2004 (1)

2001 (1)

1997 (1)

E. S. Wachman, W. Niu, and D. L. Farkas, “AOTF microscope for imaging with increased speed and spectral versatility,” Biophys. J. 73(3), 1215–1222 (1997).
[Crossref] [PubMed]

1996 (2)

Z. Malik, D. Cabib, R. A. Buckwald, A. Talmi, Y. Garini, and S. G. Lipson, “Fourier transform multi-pixel spectroscopy for quantitative cytology,” J. Microsc. 182(2), 133–140 (1996).
[Crossref]

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

1961 (1)

H. Happ and L. Genzel, “Interferenz-modulation mit monochromatischen millimeter-wellen,” Infrared Phys. 1(1), 39–48 (1961).
[Crossref]

1928 (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).
[Crossref]

Angel, S. M.

Averbuch, A.

Bar-Am, I.

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Barducci, A.

Barnett, N.

J. M. Eichenholz, N. Barnett, Y. Juang, D. Fish, S. Spano, E. Lindsley, and D. L. Farkas, “Real-time megapixel multispectral bioimaging,” Proc. SPIE 7568, 75681L (2010).
[Crossref]

Buckwald, R. A.

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3-5 μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[Crossref]

Z. Malik, D. Cabib, R. A. Buckwald, A. Talmi, Y. Garini, and S. G. Lipson, “Fourier transform multi-pixel spectroscopy for quantitative cytology,” J. Microsc. 182(2), 133–140 (1996).
[Crossref]

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Cabib, D.

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3-5 μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[Crossref]

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Z. Malik, D. Cabib, R. A. Buckwald, A. Talmi, Y. Garini, and S. G. Lipson, “Fourier transform multi-pixel spectroscopy for quantitative cytology,” J. Microsc. 182(2), 133–140 (1996).
[Crossref]

Carter, J. C.

Drew, S.

W. Huang, K. Hennrick, and S. Drew, “A colorful future of quantitative pathology: validation of Vectra technology using chromogenic multiplexed immunohistochemistry and prostate tissue microarrays,” Hum. Pathol. 44(1), 29–38 (2013).
[Crossref] [PubMed]

du Manoir, S.

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Eichenholz, J. M.

J. M. Eichenholz, N. Barnett, Y. Juang, D. Fish, S. Spano, E. Lindsley, and D. L. Farkas, “Real-time megapixel multispectral bioimaging,” Proc. SPIE 7568, 75681L (2010).
[Crossref]

Eland, K. L.

Evans, A.

F. Ghaznavi, A. Evans, A. Madabhushi, and M. Feldman, “Digital imaging in pathology: whole-slide imaging and beyond,” Annu. Rev. Pathol. 8(1), 331–359 (2013).
[Crossref] [PubMed]

Farkas, D. L.

J. M. Eichenholz, N. Barnett, Y. Juang, D. Fish, S. Spano, E. Lindsley, and D. L. Farkas, “Real-time megapixel multispectral bioimaging,” Proc. SPIE 7568, 75681L (2010).
[Crossref]

E. S. Wachman, W. Niu, and D. L. Farkas, “AOTF microscope for imaging with increased speed and spectral versatility,” Biophys. J. 73(3), 1215–1222 (1997).
[Crossref] [PubMed]

Feldman, M.

F. Ghaznavi, A. Evans, A. Madabhushi, and M. Feldman, “Digital imaging in pathology: whole-slide imaging and beyond,” Annu. Rev. Pathol. 8(1), 331–359 (2013).
[Crossref] [PubMed]

Fish, D.

J. M. Eichenholz, N. Barnett, Y. Juang, D. Fish, S. Spano, E. Lindsley, and D. L. Farkas, “Real-time megapixel multispectral bioimaging,” Proc. SPIE 7568, 75681L (2010).
[Crossref]

Frigo, M.

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93(2), 216–231 (2005).
[Crossref]

Fu, H. L.

Garini, Y.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: principles and applications,” Cytometry A 69(8), 735–747 (2006).
[Crossref] [PubMed]

Z. Malik, D. Cabib, R. A. Buckwald, A. Talmi, Y. Garini, and S. G. Lipson, “Fourier transform multi-pixel spectroscopy for quantitative cytology,” J. Microsc. 182(2), 133–140 (1996).
[Crossref]

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Genzel, L.

H. Happ and L. Genzel, “Interferenz-modulation mit monochromatischen millimeter-wellen,” Infrared Phys. 1(1), 39–48 (1961).
[Crossref]

Ghaznavi, F.

F. Ghaznavi, A. Evans, A. Madabhushi, and M. Feldman, “Digital imaging in pathology: whole-slide imaging and beyond,” Annu. Rev. Pathol. 8(1), 331–359 (2013).
[Crossref] [PubMed]

Gil, A.

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3-5 μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[Crossref]

Golub, M. A.

Guzzi, D.

Haaland, D. M.

Happ, H.

H. Happ and L. Genzel, “Interferenz-modulation mit monochromatischen millimeter-wellen,” Infrared Phys. 1(1), 39–48 (1961).
[Crossref]

Hennrick, K.

W. Huang, K. Hennrick, and S. Drew, “A colorful future of quantitative pathology: validation of Vectra technology using chromogenic multiplexed immunohistochemistry and prostate tissue microarrays,” Hum. Pathol. 44(1), 29–38 (2013).
[Crossref] [PubMed]

Huang, W.

W. Huang, K. Hennrick, and S. Drew, “A colorful future of quantitative pathology: validation of Vectra technology using chromogenic multiplexed immunohistochemistry and prostate tissue microarrays,” Hum. Pathol. 44(1), 29–38 (2013).
[Crossref] [PubMed]

Johnson, S. G.

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93(2), 216–231 (2005).
[Crossref]

Juang, Y.

J. M. Eichenholz, N. Barnett, Y. Juang, D. Fish, S. Spano, E. Lindsley, and D. L. Farkas, “Real-time megapixel multispectral bioimaging,” Proc. SPIE 7568, 75681L (2010).
[Crossref]

Katzir, N.

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Kuech, T. F.

Lastri, C.

Lavi, E.

Lavi, M.

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3-5 μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[Crossref]

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Lindsley, E.

J. M. Eichenholz, N. Barnett, Y. Juang, D. Fish, S. Spano, E. Lindsley, and D. L. Farkas, “Real-time megapixel multispectral bioimaging,” Proc. SPIE 7568, 75681L (2010).
[Crossref]

Lipson, S. G.

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3-5 μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[Crossref]

Z. Malik, D. Cabib, R. A. Buckwald, A. Talmi, Y. Garini, and S. G. Lipson, “Fourier transform multi-pixel spectroscopy for quantitative cytology,” J. Microsc. 182(2), 133–140 (1996).
[Crossref]

Lo, J. Y.

Macville, M.

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Madabhushi, A.

F. Ghaznavi, A. Evans, A. Madabhushi, and M. Feldman, “Digital imaging in pathology: whole-slide imaging and beyond,” Annu. Rev. Pathol. 8(1), 331–359 (2013).
[Crossref] [PubMed]

A. Madabhushi, “Digital pathology image analysis: opportunities and challenges,” Imaging Med. 1(1), 7–10 (2009).
[Crossref]

Malik, Z.

Z. Malik, D. Cabib, R. A. Buckwald, A. Talmi, Y. Garini, and S. G. Lipson, “Fourier transform multi-pixel spectroscopy for quantitative cytology,” J. Microsc. 182(2), 133–140 (1996).
[Crossref]

Marcoionni, P.

McNamara, G.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: principles and applications,” Cytometry A 69(8), 735–747 (2006).
[Crossref] [PubMed]

Nardino, V.

Nathan, M.

Niu, W.

E. S. Wachman, W. Niu, and D. L. Farkas, “AOTF microscope for imaging with increased speed and spectral versatility,” Biophys. J. 73(3), 1215–1222 (1997).
[Crossref] [PubMed]

Nyquist, H.

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).
[Crossref]

Palmer, G. M.

Pantanowitz, L.

L. Pantanowitz, “Digital images and the future of digital pathology,” J. Pathol. Inform. 1(1), 15 (2010).
[Crossref] [PubMed]

Pippi, I.

Ramanujam, N.

Ried, T.

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Schclar, A.

Schröck, E.

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Sinclair, M. B.

Spano, S.

J. M. Eichenholz, N. Barnett, Y. Juang, D. Fish, S. Spano, E. Lindsley, and D. L. Farkas, “Real-time megapixel multispectral bioimaging,” Proc. SPIE 7568, 75681L (2010).
[Crossref]

Stratis, D. N.

Talmi, A.

Z. Malik, D. Cabib, R. A. Buckwald, A. Talmi, Y. Garini, and S. G. Lipson, “Fourier transform multi-pixel spectroscopy for quantitative cytology,” J. Microsc. 182(2), 133–140 (1996).
[Crossref]

Timlin, J. A.

Tomlinson, S. J.

Wachman, E. S.

E. S. Wachman, W. Niu, and D. L. Farkas, “AOTF microscope for imaging with increased speed and spectral versatility,” Biophys. J. 73(3), 1215–1222 (1997).
[Crossref] [PubMed]

Werner-Washburne, M.

Wine, D.

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Young, I. T.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: principles and applications,” Cytometry A 69(8), 735–747 (2006).
[Crossref] [PubMed]

Yu, B.

Zheludev, V. A.

Annu. Rev. Pathol. (1)

F. Ghaznavi, A. Evans, A. Madabhushi, and M. Feldman, “Digital imaging in pathology: whole-slide imaging and beyond,” Annu. Rev. Pathol. 8(1), 331–359 (2013).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Spectrosc. (1)

Bioimaging (1)

Y. Garini, M. Macville, S. du Manoir, R. A. Buckwald, M. Lavi, N. Katzir, D. Wine, I. Bar-Am, E. Schröck, D. Cabib, and T. Ried, “Spectral karyotyping,” Bioimaging 4(2), 65–72 (1996).
[Crossref]

Biophys. J. (1)

E. S. Wachman, W. Niu, and D. L. Farkas, “AOTF microscope for imaging with increased speed and spectral versatility,” Biophys. J. 73(3), 1215–1222 (1997).
[Crossref] [PubMed]

Cytometry A (1)

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: principles and applications,” Cytometry A 69(8), 735–747 (2006).
[Crossref] [PubMed]

Hum. Pathol. (1)

W. Huang, K. Hennrick, and S. Drew, “A colorful future of quantitative pathology: validation of Vectra technology using chromogenic multiplexed immunohistochemistry and prostate tissue microarrays,” Hum. Pathol. 44(1), 29–38 (2013).
[Crossref] [PubMed]

Imaging Med. (1)

A. Madabhushi, “Digital pathology image analysis: opportunities and challenges,” Imaging Med. 1(1), 7–10 (2009).
[Crossref]

Infrared Phys. (1)

H. Happ and L. Genzel, “Interferenz-modulation mit monochromatischen millimeter-wellen,” Infrared Phys. 1(1), 39–48 (1961).
[Crossref]

J. Microsc. (1)

Z. Malik, D. Cabib, R. A. Buckwald, A. Talmi, Y. Garini, and S. G. Lipson, “Fourier transform multi-pixel spectroscopy for quantitative cytology,” J. Microsc. 182(2), 133–140 (1996).
[Crossref]

J. Pathol. Inform. (1)

L. Pantanowitz, “Digital images and the future of digital pathology,” J. Pathol. Inform. 1(1), 15 (2010).
[Crossref] [PubMed]

Opt. Express (2)

Proc. IEEE (1)

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93(2), 216–231 (2005).
[Crossref]

Proc. SPIE (2)

J. M. Eichenholz, N. Barnett, Y. Juang, D. Fish, S. Spano, E. Lindsley, and D. L. Farkas, “Real-time megapixel multispectral bioimaging,” Proc. SPIE 7568, 75681L (2010).
[Crossref]

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3-5 μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[Crossref]

Trans. Am. Inst. Electr. Eng. (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).
[Crossref]

Other (8)

Vectra 3.0 Quantitative pathology Imaging system user's manual (Perkin Elmer, 2015).

I. N. Sneddon, Fourier Transforms (Courier Corporation, 1995).

B. J. Lindbloom, “Spectral Computation of XYZ”, http://www.brucelindbloom.com/index.html?Eqn_Spect_to_XYZ.html .

I. T. Young, J. J. Gerbrands, and L. J. Van Vliet, Fundamentals of Image Processing (Delft University of Technology, 1998).

M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications (Springer Science & Business Media, 2009).

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Y. Garini and E. Tauber, “Spectral imaging: methods, design, and applications,” in Biomedical Optical Imaging Technologies: Design and Applications, R. Liang, ed. (Springer, 2013).

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Figures (8)

Fig. 1
Fig. 1

The Sagnac interferometer implemented as part of a spectral imaging system. M1 and M2 are mirrors, L1 is a collimating lens, L2 is a focusing lens and BS is a beam splitter. The black line represents the optical axis. The on-axis beam (green lines) has the same path for the reflectance and transmittance arms of the interferometer and therefore creates a zero OPD. An off-axis beam (purple lines) along the x-axis has a different path for the transmittance arm (solid lines) and the reflectance arm (dashed lines); hence it creates a non-zero OPD. Since the angle of the entrance beam depends on the position of the point in the sample relative to the optical axis, each point in the sample along the x-axis has a different OPD.

Fig. 2
Fig. 2

Illustration of the measurement procedure with the new system. Each strip of the image is measured while the sample is continuously moving at a constant velocity. The red box represents the area captured by the camera at three consecutive time-points. The sample travels a distance d between each two images. As a result, each point in the sample is measured a couple of time, but it is measured at different OPD that varies along the x-axis. The arrows pointing to the interferogram shown at the bottom describe this process. Therefore, for each point in the sample, an interferogram is formed by collecting data from different pixel on the camera in each captured image. The interferogram is then Fourier transformed to get the spectrum at each pixel.

Fig. 3
Fig. 3

Scheme of interferogram construction for the first k images. The captured images shown in Fig. 2 are shifted with respect to one another. The size of the shift in pixels, p, depends on the system calibration and acquisition conditions. The interferogram of each point in the sample is constructed by collecting data from different pixels that are shown along each of the red lines in the figure.

Fig. 4
Fig. 4

Scheme of the interferogram construction for the rest of the images. Note that the actual interference fringes along the scanning axis are not shown.

Fig. 5
Fig. 5

Testing the spatial resolution of the system by measuring a USAF-1951 resolution target in two different ways: 1. In the ‘direct mode’ where we take the beam splitter out of the optical path and therefore measure a normal image and 2. A gray-level image calculated from the spectral image measured for the same sample. As can be seen, along the horizontal axis (which is the scanning direction), there is a slight broadening of the spectral image (magenta) relative to the direct mode image (green). In the vertical axis, the spectral (red) and the direct mode (blue) images have the same resolution. Markers represent the pixel intensities and the lines are the Gaussian fits.

Fig. 6
Fig. 6

Spectral measurements of a series of band-pass filters (450-800nm in steps of 50nm. FWHM of 10 ± 2nm). The measured peak wavelength and FWHM for each filter are shown in the plot. The spectral resolution (calculated by deconvolving the measured FWHM and the real filter FWHM) was found to change from ~5 nm at λ = 450 nm to ~17 nm at λ = 800 nm.

Fig. 7
Fig. 7

(A) The reconstructed RGB image from the spectral image measured from the image of the BIU logo (upper inset), as measured from a smartphone screen, scale bar is 500 μm. The image consists of 2605x2175 pixels, which is larger than the size of the camera and demonstrates the scanning capabilities of the system. The inset at the bottom right shows a zoom-in of a single green smartphone diode. The image reflects various quality parameters of the image, including the sharpness, uniformity, noise uniformity, lack of image distortion and uniformity of the spectral measurement. (B) The normalized spectra measured at different places on the image, denoted by numbers in (A). The circles are the measured data, solid lines are a smoothed function. These spectra were compared to the spectra from the same smartphone screen measured with a spectrometer and demonstrated excellent agreement.

Fig. 8
Fig. 8

(A) The reconstructed giant white-balanced RGB image (~13,000 x 6,500 pixels, 85 mega pixels) of a bone marrow tissue section sample of size ~7 mm X 3.5 mm. The inset at the bottom left shows a comparison of a small part of the few cells that were measured with a normal RGB camera image (left) and spectral-reconstructed image (right). The upper rectangular frame represents the area of a single FOV that can be captured by the camera. (B) Zoom-in on the framed area shown in (A). The inset shows the spectra of three points marked in the image by the colored arrows. Note the differences in the spectra. Except for the different intensities, there are different spectral features that can be shown in the spectral shape at certain ranges and the peak position.

Equations (5)

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l=Cθ
I d (l)=0.5[ I in (σ) dσ+ I in (σ)cos(2πlσ)dσ ]
HG(x)=0.54+0.46cos(πl/L)
v= spx τ
v=d f camera

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