Abstract

A significant part of the uniformity degradation in the acquired hyperspectral images can be attributed to the coregistration distortions and spectrally and spatially dependent resolution arising from the misalignments and the operation principle of the spectrograph based hyperspectral imaging system. The aim of this study was the development and validation of a practical method for characterization of the geometric coregistration distortions and position dependent resolution. The proposed method is based on modeling the imaging system response to several affordable reference objects. The results of the characterization can be used for calibration of the acquired images or as a tool for assessment of the expected errors in various hyperspectral imaging systems.

© 2013 OSA

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References

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    [CrossRef]
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    [CrossRef]
  21. J. Katrašnik, F. Pernuš, and B. Likar, “Deconvolution in Acousto-Optical Tunable Filter Spectrometry,” Appl. Spectrosc.64(11), 1265–1273 (2010).
    [CrossRef] [PubMed]

2012 (2)

Ž. Špiclin, M. Bürmen, F. Pernuš, and B. Likar, “Characterization and modelling of the spatially- and spectrally-varying point-spread function in hyperspectral imaging systems for computational correction of axial optical aberrations,” Proc. SPIE8215, 82150R, 82150R-9 (2012).
[CrossRef]

T. Skauli, “An upper-bound metric for characterizing spectral and spatial coregistration errors in spectral imaging,” Opt. Express20(2), 918–933 (2012).
[CrossRef] [PubMed]

2011 (1)

2010 (2)

2009 (2)

2008 (2)

2007 (1)

D. Schlapfer, J. Nieke, and K. I. Itten, “Spatial PSF Nonuniformity Effects in Airborne Pushbroom Imaging Spectrometry Data,” IEEE Trans. Geosci. Rem. Sens.45(2), 458–468 (2007).
[CrossRef]

2004 (2)

J. Zadnik, D. Guerin, R. Moss, A. Orbeta, R. Dixon, C. G. Simi, S. Dunbar, and A. Hill, “Calibration procedures and measurements for the COMPASS hyperspectral imager,” Proc. SPIE5425, 182–188 (2004).
[CrossRef]

D. Kohler, W. Bissett, R. Steward, and C. Davis, “New approach for the radiometric calibration of spectral imaging systems,” Opt. Express12(11), 2463–2477 (2004).
[CrossRef] [PubMed]

2003 (1)

G. Polder, G. van der Heijden, L. Keizer, and I. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc.11(1), 193–193 (2003).
[CrossRef]

1990 (1)

T. G. Chrien, R. O. Green, and M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE1298, 37–49 (1990).
[CrossRef]

1968 (1)

E. E. Whiting, “An empirical approximation to the Voigt profile,” J. Quant. Spectroc. Rad.8(6), 1379–1384 (1968).
[CrossRef]

Alonso, L.

Bissett, W.

Bürmen, M.

Ž. Špiclin, M. Bürmen, F. Pernuš, and B. Likar, “Characterization and modelling of the spatially- and spectrally-varying point-spread function in hyperspectral imaging systems for computational correction of axial optical aberrations,” Proc. SPIE8215, 82150R, 82150R-9 (2012).
[CrossRef]

Busetto, L.

Chrien, T. G.

T. G. Chrien, R. O. Green, and M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE1298, 37–49 (1990).
[CrossRef]

Claxton, C. D.

Cogliati, S.

Colombo, R.

Crosta, G. F.

Davis, C.

Dixon, R.

J. Zadnik, D. Guerin, R. Moss, A. Orbeta, R. Dixon, C. G. Simi, S. Dunbar, and A. Hill, “Calibration procedures and measurements for the COMPASS hyperspectral imager,” Proc. SPIE5425, 182–188 (2004).
[CrossRef]

Dunbar, S.

J. Zadnik, D. Guerin, R. Moss, A. Orbeta, R. Dixon, C. G. Simi, S. Dunbar, and A. Hill, “Calibration procedures and measurements for the COMPASS hyperspectral imager,” Proc. SPIE5425, 182–188 (2004).
[CrossRef]

Eastwood, M. L.

T. G. Chrien, R. O. Green, and M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE1298, 37–49 (1990).
[CrossRef]

Esmonde-White, F. W. L.

Esmonde-White, K. A.

Feng, Y.

Green, R. O.

T. G. Chrien, R. O. Green, and M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE1298, 37–49 (1990).
[CrossRef]

Griffiths, P. R.

Guanter, L.

Guerin, D.

J. Zadnik, D. Guerin, R. Moss, A. Orbeta, R. Dixon, C. G. Simi, S. Dunbar, and A. Hill, “Calibration procedures and measurements for the COMPASS hyperspectral imager,” Proc. SPIE5425, 182–188 (2004).
[CrossRef]

Hill, A.

J. Zadnik, D. Guerin, R. Moss, A. Orbeta, R. Dixon, C. G. Simi, S. Dunbar, and A. Hill, “Calibration procedures and measurements for the COMPASS hyperspectral imager,” Proc. SPIE5425, 182–188 (2004).
[CrossRef]

Itten, K. I.

D. Schlapfer, J. Nieke, and K. I. Itten, “Spatial PSF Nonuniformity Effects in Airborne Pushbroom Imaging Spectrometry Data,” IEEE Trans. Geosci. Rem. Sens.45(2), 458–468 (2007).
[CrossRef]

Katrašnik, J.

Kaufmann, H.

Keizer, L.

G. Polder, G. van der Heijden, L. Keizer, and I. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc.11(1), 193–193 (2003).
[CrossRef]

Kohler, D.

Likar, B.

Ž. Špiclin, M. Bürmen, F. Pernuš, and B. Likar, “Characterization and modelling of the spatially- and spectrally-varying point-spread function in hyperspectral imaging systems for computational correction of axial optical aberrations,” Proc. SPIE8215, 82150R, 82150R-9 (2012).
[CrossRef]

J. Katrašnik, F. Pernuš, and B. Likar, “Deconvolution in Acousto-Optical Tunable Filter Spectrometry,” Appl. Spectrosc.64(11), 1265–1273 (2010).
[CrossRef] [PubMed]

Meroni, M.

Migliavacca, M.

Moreno, J.

Morris, M. D.

Moss, R.

J. Zadnik, D. Guerin, R. Moss, A. Orbeta, R. Dixon, C. G. Simi, S. Dunbar, and A. Hill, “Calibration procedures and measurements for the COMPASS hyperspectral imager,” Proc. SPIE5425, 182–188 (2004).
[CrossRef]

Nieke, J.

D. Schlapfer, J. Nieke, and K. I. Itten, “Spatial PSF Nonuniformity Effects in Airborne Pushbroom Imaging Spectrometry Data,” IEEE Trans. Geosci. Rem. Sens.45(2), 458–468 (2007).
[CrossRef]

Orbeta, A.

J. Zadnik, D. Guerin, R. Moss, A. Orbeta, R. Dixon, C. G. Simi, S. Dunbar, and A. Hill, “Calibration procedures and measurements for the COMPASS hyperspectral imager,” Proc. SPIE5425, 182–188 (2004).
[CrossRef]

Panigada, C.

Pernuš, F.

Ž. Špiclin, M. Bürmen, F. Pernuš, and B. Likar, “Characterization and modelling of the spatially- and spectrally-varying point-spread function in hyperspectral imaging systems for computational correction of axial optical aberrations,” Proc. SPIE8215, 82150R, 82150R-9 (2012).
[CrossRef]

J. Katrašnik, F. Pernuš, and B. Likar, “Deconvolution in Acousto-Optical Tunable Filter Spectrometry,” Appl. Spectrosc.64(11), 1265–1273 (2010).
[CrossRef] [PubMed]

Polder, G.

G. Polder, G. van der Heijden, L. Keizer, and I. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc.11(1), 193–193 (2003).
[CrossRef]

Rossini, M.

Sang, B.

Schlapfer, D.

D. Schlapfer, J. Nieke, and K. I. Itten, “Spatial PSF Nonuniformity Effects in Airborne Pushbroom Imaging Spectrometry Data,” IEEE Trans. Geosci. Rem. Sens.45(2), 458–468 (2007).
[CrossRef]

Segl, K.

Shao, L.

Simi, C. G.

J. Zadnik, D. Guerin, R. Moss, A. Orbeta, R. Dixon, C. G. Simi, S. Dunbar, and A. Hill, “Calibration procedures and measurements for the COMPASS hyperspectral imager,” Proc. SPIE5425, 182–188 (2004).
[CrossRef]

Skauli, T.

Špiclin, Ž.

Ž. Špiclin, M. Bürmen, F. Pernuš, and B. Likar, “Characterization and modelling of the spatially- and spectrally-varying point-spread function in hyperspectral imaging systems for computational correction of axial optical aberrations,” Proc. SPIE8215, 82150R, 82150R-9 (2012).
[CrossRef]

Staunton, R. C.

Steward, R.

van der Heijden, G.

G. Polder, G. van der Heijden, L. Keizer, and I. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc.11(1), 193–193 (2003).
[CrossRef]

Whiting, E. E.

E. E. Whiting, “An empirical approximation to the Voigt profile,” J. Quant. Spectroc. Rad.8(6), 1379–1384 (1968).
[CrossRef]

Xiang, Y.

Young, I.

G. Polder, G. van der Heijden, L. Keizer, and I. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc.11(1), 193–193 (2003).
[CrossRef]

Zadnik, J.

J. Zadnik, D. Guerin, R. Moss, A. Orbeta, R. Dixon, C. G. Simi, S. Dunbar, and A. Hill, “Calibration procedures and measurements for the COMPASS hyperspectral imager,” Proc. SPIE5425, 182–188 (2004).
[CrossRef]

Appl. Opt. (1)

Appl. Spectrosc. (3)

IEEE Trans. Geosci. Rem. Sens. (1)

D. Schlapfer, J. Nieke, and K. I. Itten, “Spatial PSF Nonuniformity Effects in Airborne Pushbroom Imaging Spectrometry Data,” IEEE Trans. Geosci. Rem. Sens.45(2), 458–468 (2007).
[CrossRef]

J. Near Infrared Spectrosc. (1)

G. Polder, G. van der Heijden, L. Keizer, and I. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc.11(1), 193–193 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Quant. Spectroc. Rad. (1)

E. E. Whiting, “An empirical approximation to the Voigt profile,” J. Quant. Spectroc. Rad.8(6), 1379–1384 (1968).
[CrossRef]

Opt. Express (4)

Proc. SPIE (3)

Ž. Špiclin, M. Bürmen, F. Pernuš, and B. Likar, “Characterization and modelling of the spatially- and spectrally-varying point-spread function in hyperspectral imaging systems for computational correction of axial optical aberrations,” Proc. SPIE8215, 82150R, 82150R-9 (2012).
[CrossRef]

J. Zadnik, D. Guerin, R. Moss, A. Orbeta, R. Dixon, C. G. Simi, S. Dunbar, and A. Hill, “Calibration procedures and measurements for the COMPASS hyperspectral imager,” Proc. SPIE5425, 182–188 (2004).
[CrossRef]

T. G. Chrien, R. O. Green, and M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE1298, 37–49 (1990).
[CrossRef]

Other (6)

A. Kramida and Y. Ralchenko, J. Reader, and N. A. Team, “NIST Atomic Spectra Database (version 5.0),” (National Institute of Standards and Technology, Gaithersburg, MD., 2012).

C. T. Kelley, Iterative methods for optimization (Society for Industrial Mathematics, Philadelphia, 1999).

R. Fletcher, Practical methods of optimization (Wiley, Chichester, 2000).

R. A. Schowengerdt, Remote Sensing: Models and Methods for Image Processing, 3rd ed. (Academic Press, 2006).

R. N. Jørgensen and F. Risø, The VTTVIS line imaging spectrometer: principles, error sources, and calibration (Risø National Laboratory, 2002).

C. D. Cantrell, Modern Mathematical Methods for Physicists and Engineers (Cambridge University Press, Cambridge, 2000).

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Figures (11)

Fig. 1
Fig. 1

Example of a spectral (Ne) (a) and a spatial (b) reference image.

Fig. 2
Fig. 2

Weighted acquired spectra of the three utilized reference sources. The problem of low spectral resolution is clearly demonstrated by the two recorded spectral peaks of the Hg(Ar) lamp. The spectral peak Hg-I corresponds to the single Hg spectral line at 546.07 nm while the Hg-II peak is a response to two Hg spectral lines at 576.96 nm and 579.07 nm, unresolvable due to the limited instrument resolution and discrete sampling. This is the reason for the difference between the number of observed peaks and the number of tabulated spectral lines. Furthermore, at shorter wavelengths peaks are approximately Gaussian. However, towards the NIR end of the observed spectral range, the spectral peaks (e.g. Ar-I at 965.78 nm) become wider and their tails longer than the Gaussian function would model.

Fig. 3
Fig. 3

Illustration of the selected spatial region.

Fig. 4
Fig. 4

Schematic of the experimental setup (a). Spectralon tile (T), long-pass filter (F), diffuser (D). The spatial reference object (b).

Fig. 5
Fig. 5

Extracted image positions of two spectral lines (a, b) and the corresponding positions estimated by the computed model, clearly demonstrate subpixel rotation of the image due to misalignment of the camera and the spectrograph slit, and the bending of the spectral lines which is in agreement with previously published work [1]. Furthermore, the spectral axis nonlinearity is evident from spectral dependency of the spectral tuning function residual δZS (c). Extracted positions of the two outermost edges at different spectral channels and the corresponding edge positions estimated by the computed characterization model (d, e) suggest rotation and the wavelength dependent magnification. The higher order spatial tuning function residual δZSi (f).

Fig. 6
Fig. 6

Plots of the Voigt profile parameter interpolation surfaces ΓL(u,w) (a), and ΓG(u,w) (b) show the increasing influence of Lorentzian broadening with longer wavelength. Spectral resolution in terms of Half Width at Half Maximum HWHM of the Voigt profile (c). At the NIR end of the utilized spectral range the resolution is significantly lower than at shorter wavelengths.

Fig. 7
Fig. 7

Normalized SiRFs at different image locations, plotted on 32 pixel wide intervals marked by black vertical lines. Best resolution is exhibited in the central part of the acquired image.

Fig. 8
Fig. 8

(a) Asymmetry and complexity of the SiRF are easily observed in plots of the SiRF for spatial channel 742 at two wavelengths corresponding to spectral channels 10 and 570. (b) Quality of the proposed model fit and wavelength dependent shifts of the edges due to coregistration errors are evident from overlay of the acquired (black) and the estimated (red) profiles of two edges in the image of the validation object. Plotted profiles correspond to the two depicted SiRFs.

Fig. 9
Fig. 9

Accuracy of the forward tuning function and SRF estimation are presented by comparison of the acquired image and the estimated image of the spectral and spatial validation objects. Estimated spectrum in the central part of the Kr validation image and the fit error expressed as a difference between the estimated and acquired spectrum (a). Estimated image profile in the central part of the spatial validation image and the fit error computed by subtracting the estimated and the acquired profile (b).

Fig. 10
Fig. 10

Residual misalignment between the measured and the true edge positions. Centers represent the mean error and the error bars correspond to the standard deviation. Dashed line denotes the reference object uncertainty. The edge locations correspond to the edges in the profile shown in Fig. 9(b).

Fig. 11
Fig. 11

The effects of the calibration observed in the spectral and spatial validation images. For better visualization of the small coregistration errors only spectra and spatial profiles limited to image subregions are shown. (a) Spectra of the 760.15 nm and 769.45 nm Kr spectral lines at spatial channels 10 and 990 corresponding to true spatial positions 2.07 mm and 152.16 mm. Due to coregistration errors, the spectra in the acquired image are shifted by approximately 0.25 pixel. (b) After transforming the acquired image into the object space the image is calibrated to real physical units and the coregistration improves. Similar observation holds for the spatial validation image. (c) Plot of the three spatial validation image profiles of a single edge at spectral channels 17, 282 and 555 corresponding to wavelengths 540 nm, 750 nm and 970 nm clearly shows wavelength dependent spatial distortions. (d) After the calibration the profiles are spatially aligned.

Tables (1)

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Table 1 The wavelength prediction error statistics of the four Kr spectral lines.

Equations (20)

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I(u,w)= D(u,w) [ T(g(θ,λ))SRF(υ,ω)SiRF(υ,ω) ] (υ,ω)dυdω+ε(u,w)
S A (u,w)= D(u,w) [ T S ( g S (θ,λ))SRF(υ,ω) ](υ,ω) dυdω+ ε S (u,w),
S i A (u,w)= D(u,w) [ T Si ( g Si (θ,λ))SiRF(υ,ω) ](υ,ω) dυdω+ ε Si (u,w).
S M ,l ,u (w)=δuδw j=1 J l α l, j V(w w 0,l,j ,u , γ G (u, w 0,l,j ,u ), γ L (u, w 0,l,j ,u ))+ k=0 K β l,k ,u w k ,
χ S,u = 1 L l=1 L { [ 1wcc( S M,l ,u (w), S A,l ,u (w), μ l (w)) ]+wsse( S M,l ,u (w), S A,l ,u (w), μ l (w)) } ,
wcc( s M , s A ,μ)= w=1 W μ(w)( s A (w) s A )( s M (w) s M ) [ w=1 W (μ(w) ( s A (w) s A ) 2 w=1 W μ(w) ( s M (w) s M ) 2 ] 1/2 ,
wsse( s M , s A ,μ)= w=1 W μ(w) [ s A (w) s M (w)] 2 / w=1 W μ(w) .
T Si ( g Si (θ,λ))= c M H(τ(υ u 0 ))+ c A ,
SiRF(υ)= m=1 M ρ m N(υ; μ G, m , σ m ) .
[ T Si ( g Si (θ,λ))SiRF ](υ,ω)= 1 2 c M ( 1+ m=1 M ρ m erf( τ (υ( μ G, m + u 0 ) 2 σ m ) )+ c A .
S i A ,e , w (u)=δuδw( 1 2 c M ,e ( 1+ m=1 M ρ m erf( τ e (u( μ G, m + u 0,e ) 2 σ m ) )+ c A,e )+ ε Si ,w (u)
m=1 M ρ m =1, m=1 M ρ m μ G, m =0.
Δ u R =round( 1 2 1 W(E-1) w=1 W e=1 E-1 | u ˜ 0,e+1,w u ˜ 0,e,w | ),
{ u 0,Opt,r , ρ Opt,r , μ G, Opt,r , σ Opt,r }=argmin( η r ε Si,r 2 ( η r , u 0,r , ρ r , μ G, r , σ r , c M ,r , c A,r ) ),
γ G (υ,ω) Γ G (υ,ω),
γ L (υ,ω) Γ L (υ,ω),
λ Z S (υ,ω).
θ Z Si (υ,ω).
ω T S (θ,λ),
υ T Si (θ,λ).

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