Illuminant Influence On The Reconstruction Of NIR Spectra 3371 0deec5231f9b126b3b000000

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Illuminant Influence on the Reconstruction of

NIR Spectra

Meritxell Vilasecaa, Jaume Pujola, Montserrat Arjonaa, and Francisco Martínez-Verdúb

aCenter for Sensors, Instrumentation and Systems Development (CD6),

Dept. of Optics and Optometry, Universitat Politècnica de Catalunya

Terrassa, Barcelona, Spain

bDept. Interuniversitari d’Òptica, Universitat d’Alacant

Alacant, Spain

Abstract

In order to recover spectral reflectances or transmittances

using a multispectral imaging based technique, it is

necessary to know the spectral radiance of the illuminant

used to light the samples in the acquisition process. In this

study, we analyzed the influence of the spectral

distribution of the illuminant on the reconstruction of

spectral reflectances in the near infrared region of the

spectrum (NIR). We considered a set of 30 textile samples

with different spectral reflectance in this region. We tested

the performance of a principal component analysis (PCA)

based method and a non-linear estimation method (NLE),

which allow us to obtain the spectral reflectance of

samples in the NIR region from a small number of

measurements performed with a CCD camera. Using

numerical simulation, we analyzed the number and shape

of the optimum filters that need to be used in the

acquisition channels in order to obtain good spectral

reconstructions under several lighting conditions. Finally,

we studied the quality of the reconstructions with a set of

commercially available filters which are similar to the

optimum filters obtained in the simulations. The results

obtained show that the reconstruction does not depend

heavily on the illuminant used. This indicates that, with the

same set of filters, we can obtain good reconstructions for

different types of illuminant.

Introduction

Conventional CCD cameras1,2 have maximum spectral

sensitivity in the visible region of the spectrum.

Nevertheless, CCD cameras with improved response in the

near infrared (NIR) are currently manufactured and their

spectral sensitivity is clearly significant up to 1000 nm.

Therefore, this standard instrumentation can be used in

order to obtain spectral information of samples in the NIR

region (800 – 1000 nm), which is not usually available

with conventional spectrophotometers. Standard

spectrophoto-meters normally have their response limited

to the visible range and require additional sensors to detect

energy coming from the NIR (for example, InGaAs), which

can significantly increase their cost. The spectral

information included in the NIR region is in general

directly related to the constituents of a material. Therefore,

it is used as an analytical tool in industry and research, and

is known as NIR technology.3 The applications include

agriculture, the food industry, medical applications,

military applications, the chemical industry etc.

Multispectral imaging4-7 allows us to obtain the

reflectance or transmittance spectra of samples using

conventional CCD camera measurements. This technique

uses different acquisition channels from which several

images of the analyzed sample are obtained. Because of

the different spectral response of the channels, the obtained

images hold spectral information of the acquired scene. It

is therefore possible to calculate the spectral reflectance or

transmittance of the original measured sample. The

multispectral imaging based methods need all the spectral

variables involved in the acquisition process to be known.

These variables are; the spectral radiance of the illuminant

used, the spectral transmittance of the filters which define

each of the acquisition channels and the spectral sensitivity

of the CCD camera. After selecting the CCD camera, we

can study which illuminants and filters may be used in

order to obtain the best reconstruction results of the set of

considered samples. Since the mathematical methods used

perform approximations, the factors mentioned may yield

different quality reconstructions.

In this work we studied the performance of two

different spectral reconstruction methods, principal

component analysis (PCA)6,8-10 and a non-linear estimation

method (NLE),11,12 under several lighting conditions. The

considered illuminants were of the blackbody type with

color temperatures between 1000 K and 16000 K. By

numerical simulation, we analyzed the shape of the

optimum filters which must be placed in front of the

camera in order to obtain good reconstructions of the

reflectance spectra of different samples for the tested

illuminants. After that, we studied the influence of the

illuminant on the quality of the reconstruction using

commercially available filters similar to the optimum

filters used in the simulations.

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Spectral Reconstruction Methods

The reconstruction process used in multispectral imaging

based methods is summarized in Figure 1. A multi-channel

image of an original object is acquired by placing a

selected set of filters in front of the camera. After that, a

spectral reconstruction method is applied and the

reconstructed spectral reflectance of the sample is

obtained.

Figure 1. Schematic view of the acquisition system and the final

spectral reconstruction step.

There are several spectral reconstruction methods

based on interpolation or estimation methods.4-7 The latter

include linear methods, NLE or PCA methods. In this work

we analyzed the performance of a PCA and an NLE

method. In previous works10,15 we showed how these

methods yield the best spectral reconstruction results in the

NIR region.

In order to use these methods, it is necessary to know a

set of spectral reflectances similar to the curves that we

want to reconstruct. The set of n known spectral

reflectances is represented by a n x p matrix called Or.

The camera responses for the acquisition channels can

be expressed in matrix notation as follows:

Cr X = (1)

where X is a column vector which represents the m

responses of the camera to a sample, r is a column vector

(n components) representing the spectral reflectance of the

sample, and C is a m

n matrix in which each row is the

spectral sensitivity of a different acquisition channel, that

is, i(

l)Fi(

l)S(

l) with i=1,.., m and l=1,...,n, i(

l) being the

spectral radiance of the illuminant, Fi(

l) the transmittance

of the filters used, and S(

l) the sensitivity of the CCD

camera.

The PCA method associates the matrix Or to a vector

space and its characteristic vectors can be calculated. Thus,

each spectral reflectance curve can be obtained as a linear

combination of the largest characteristic vectors:

rqr2r1Mrec vvvrr

ξβα

++++≈ ... , q<n (2)

where rrec is the reconstructed spectral reflectance, rM is the

mean spectral reflectance of the curves belonging to Or,

vr1, vr2,..., vrq are the characteristic vectors and

,..,

are

scalar coefficients. They can be experimentally determined

relating the camera responses for each sample to the

characteristic vectors, that is, combining Eqs. (1) and (2):

r2r1

MCvCvCvCrCrX

ξβα

++++≈= ... , q<n (3)

On the other hand, the NLE method used supposes that

a matrix DNL exists and that it provides the spectral

reflectances from:

NLNLrec XDr = (4)

where XNL is a column vector which represents a complete

second order polynomial calculated using the camera

responses, that is,

[]

322121

1321 X XX XX X X X X X X1 X=

X (5)

The matrix DNL can be calculated using the

pseudoinverse technique,5,13,14 taking into account the

reflectance spectra belonging to the matrix Or:

)( −

NLNL

NLrNL XXXOD (6)

In order to evaluate the quality of the reconstruction of

the analyzed spectra we use two different parameters :

Percentage of Reconstruction:

100

)(











−

−= ∑

∑

max

min

max

min

rec

(7)

Root Mean Square Error:

2/1

)(

1









−= ∑max

min

rec

RMSE

(8)

Data

In order to perform the simulations and the optimization

process we considered a matrix Or composed of 30 spectral

reflectance curves corresponding to textile samples (Figure

2). We considered the spectral data between 800 and 1000

nm in 10 nm steps. Therefore, each curve was made up of

21 components. The CCD camera used was a JAI CV-M10

progressive scan camera (Figure 3).

The analyzed illuminants were blackbody or Planckian

type (specifically graybody radiators) with the following

color temperatures: 1000, 1500, 1800, 1850, 1900, 2000,

2852, 3371, 4000, 5000, 6000, 7000, 8000, 9000, 12000,

13000, 14000 and 16000 K (Figure 4). 2852 and 3371 K

correspond to the color temperatures of commercial

available sources. The total emission of the illuminants

was normalized to a specific value of radiance (105

W/sr*m2) in order to obtain simulated lamps with the same

radiant flux. In the case of the PCA method, it can be seen

that the reconstruction results only depend on the relative

emission of the illuminant, that is, its color temperature.

Unlike PCA, the results provided by the NLE method have

a dependency on the absolute emission of the illuminant as

well as the color temperature. In order to take into account

this dependency we have also analyzed the NLE method

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under the influence of some illuminants with color

temperature Tc = 3371 K but different radiance values

(specifically 103, 104, 106 and 107 W/sr*m2).

Figure 2. Spectral reflectance curves of 8 representative samples

belonging to the matrix Or.

Figure 3. Experimental relative spectral sensitivity of the camera

JAI CV-M10.

In the first part of the numerical simulation we used

five equi-spaced Gaussian filters in the 800-1000 nm

region with variable spectral bandwidth, in order to obtain

simple transmittance profiles and therefore available

commercial filters. In a previous work we demonstrated

that five filters were enough to achieve good

reconstructions in the NIR region10,15. The transmittance of

each simulated filter was:























−

−=

2ln4exp)( FWHM

TT MAX

λλ

(9)

where TMAX (considered 1 in this study) is the maximum

height of the Gaussian peak,

0 is the wavelength

corresponding to the maximum (center) of the Gaussian

and FWHM is the full width at half maximum of the

Gaussian. The parameter FWHM was considered the

optimization parameter. In order to determine the shape of

the optimum filters, it was increased progressively in the

same way for all the channels and the value providing the

best reconstruction for the spectral curves belonging to Or

was chosen.

Figure 4. Spectral radiance of the analyzed illuminants

normalized to 105 W/sr*m2.

Figure 5. Spectral transmittance of the real interference filters.

After the optimizations with simulated Gaussian

filters, we used real commercial filters (Thermo Corion

interference filters) in order to evaluate the influence of the

illuminants in the reconstructions. These filters were

chosen taking into account the shape of the optimum

Gaussian filters obtained. According to the results, the

FWHM of the filters should be approximately 70 nm. The

transmittance of the five real interference filters is shown

in Figure 5.

Results

1. Reconstructions with the Simulated Gaussian Filters

In order to determine the shape of the optimum equi-

spaced Gaussian filters and therefore to obtain the best

reconstruction results under all the analyzed lighting

conditions, we performed a numerical simulation using the

two proposed reconstruction methods. The best filters were

determined by searching for the minimum mean RMSE of

the curves belonging to the matrix Or. Table 1 and Table 2

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538

show the obtained results for the PCA and the NLE

methods using illuminants with different color

temperatures and radiance 105 W/sr*m2. The obtained

reconstruction results using the NLE method and

illuminants of color temperature Tc = 3371 K with

different radiance values are shown in Table 3.

In the PCA method, the optimizations using

illuminants with higher temperature yield optimum filters

with smaller FHWM. The parameter Prec decreases with the

color temperature, and RMSE increases. Using the NLE

method, there is no clear relationship between the color

temperature and the FHWM of the optimum filters.

Similarly, the simulations performed with illuminants of

color temperature Tc = 3371K with different radiance

values provide results that do not bear any relationship to

the emitted radiance.

In both methods there is a stabilization of the optimum

spectral bandwidth of the filters for illuminants of color

temperature Tc = 5000 K – 6000 K or more. This can be

explained by the spectral emission of the illuminants in the

NIR region. Because the illuminants with large color

temperature have the maximum emission peak located at

short wavelengths, they have a similar decreasing spectral

distribution between 800 and 1000 nm.

The results obtained can be explained as follows. The

PCA method is a linear method whose simulation results

are described by equation (3). The explicit form of this

equation is:

...

1++= ∑∑∑

λλλ

λλλλ

vsFirsFirsFi iMii (10)

Table 1. Reconstruction results using the PCA method,

the simulated Gaussian filters and illuminants with

different color temperatures.

Tc (K) FWHM Mean Prec

Mean (RMSE*100)

1000 122 99.996 0.170

1500 97 99.996 0.183

1800 87 99.995 0.191

1850 85 99.995 0.193

1900 82 99.995 0.194

2000 80 99.995 0.197

2852 66 99.995 0.215

3371 61 99.994 0.223

4000 59 99.994 0.229

5000 56 99.994 0.237

6000 75 99.994 0.242

7000 54 99.994 0.245

8000 54 99.993 0.248

9000 54 99.993 0.250

12000 54 99.993 0.253

13000 54 99.993 0.254

14000 52 99.993 0.255

16000 52 99.993 0.256

Table 2. Reconstruction results using the NLE method,

the simulated Gaussian filters and illuminants with

different color temperatures.

Tc (K) FWHM Mean Prec

Mean (RMSE*100)

1000 66 100 0.032

1500 92 100 0.014

1800 38 100 0.014

1850 89 100 0.014

1900 38 100 0.013

2000 82 100 0.015

2852 80 100 0.016

3371 78 100 0.016

4000 80 100 0.016

5000 103 100 0.016

6000 103 100 0.017

7000 97 100 0.016

8000 99 100 0.016

9000 97 100 0.016

12000 101 100 0.016

13000 103 100 0.016

14000 99 100 0.016

16000 101 100 0.016

Table 3. Reconstruction results using the NLE method,

the simulated Gaussian filters and illuminants of Tc =

3371K with different radiance values.

Radiance

(W/sr*m2)

FWHM Mean Prec Mean (RMSE*100)

103 45 100 0.025

104 80 100 0.016

105 78 100 0.016

106 49 100 0.020

107 96 100 0.024

In order to obtain similar results in the optimization

process of the filters for any sample, it is necessary to have

similar values of the term i

for the different analyzed

illuminants (or, by extension, the terms i

and i

etc.). Figure 6 shows these spectral products for a

particular sample belonging to the matrix Or. While

spectral products with different shape, corresponding to

specific illuminants, have different optimization results,

similarities in these spectral curves are translated to similar

spectral bandwidths of the obtained optimum filters.

On the other hand, the shape of these products does

not explain the behavior found in the NLE method. This

method uses the pseudoinverse technique which computes

the inverse of a nonsquare matrix and which, in general,

has singularities. The method searches for a least squares

solution. Therefore, the obtained results are very sensitive

to input variations and may present considerable

oscillations.

IS&T's 2003 PICS Conference

539

Figure 6. Spectral curve r

of the sample S3 belonging to Or.

2. Reconstructions with the Real Filters

In the last section we have presented optimizations

performed with five simulated Gaussian filters. We have

seen that the spectral bandwidth of the optimum filters

depends on the considered illuminant for both analyzed

methods. Taking into account that incandescent or halogen

lamps, which are used in many devices, have color

temperatures within the 2800–3100 K range, we can

consider the results obtained for the illuminants with color

temperatures 2852 K and 3371 K as optimum. Using the

PCA method, the spectral bandwidth of the optimum filters

for these two illuminants are 66 nm and 78 nm

respectively. In the case of the NLE method, the FWHM

values are 80 nm and 78 nm. When ones uses the

illuminants of color temperature 3371 K with different

radiance values, the optimum filters have an FWHM of

between 45 nm and 96 nm. In conventional commercial

catalogues of various manufacturers we can find common

interference filters with the following spectral bandwidths

(FWHM): 1.5, 3, 10, 25, 40 and 70 nm. In almost all the

cases considered, the one most similar to those obtained in

the simulation process is the filter with a FWHM value of

70 nm. We acquired five filters with these spectral features

included in the analyzed range (Thermo Corion

interference filters), that is, the NIR region. The

transmittance of these filters is presented in the data

section (Figure 5). We can now consider how the

reconstructions use these filters under the influence of the

different illuminants. Table 4 shows the reconstruction

results obtained for the PCA method with some illuminants

of different color temperatures, and the results for the NLE

method are presented in Table 5. Table 6 shows the

reconstruction results for the NLE method under the

influence of the illuminants of color temperature 3371 K

with different radiance values.

While, with the PCA method, the RMSE parameter

increases when the color temperature is increased (as we

found in the case of the Gaussian filters), the results are

almost constant for the different illuminants analyzed with

the NLE method (except for the illuminant with color

temperature 1000 K). Using the NLE method and

illuminants of color temperature 3371 K with different

radiance values, the results obtained for the RMSE

parameter are almost the same in all the analyzed cases,

except for the illuminant with a radiance value of 107

W/sr*m2, for which a worse RMSE was found.

Table 4. Reconstruction results using the PCA method,

the five real interference filters and illuminants with

different color temperatures.

Tc Mean Prec Mean (RMSE*100)

1000 99.995 0.184

2000 99.992 0.238

2852 99.988 0.280

3371 99.985 0.302

5000 99.979 0.351

16000 99.966 0.443

Table 5. Reconstruction results using the NLE method,

the five real interference filters and illuminants with

different color temperatures.

Tc Mean Prec Mean (RMSE*100)

1000 100 0.044

2000 100 0.016

2852 100 0.016

3371 100 0.017

5000 100 0.017

16000 100 0.018

Table 6. Reconstruction results using the NLE method,

with five real interference filters and illuminants of Tc

= 3371K with different radiance values.

Radiance

(W/sr*m2)

Mean Prec Mean (RMSE*100)

103 100 0.018

104 100 0.017

105 100 0.017

106 100 0.017

107 100 0.024

In general, even when there are variations in the

results, they are not significant. All the performed

reconstructions have Prec > 99.9 % and RMSE < 1. In a

previous work it was demonstrated that these values

guarantee acceptable reconstructions of the samples in the

NIR region10,15. Therefore, the set of commercial analyzed

filters can be used to obtain spectral reflectance curves

under the influence of all the analyzed illuminants.

Conclusion

In this work, we studied the influence of the illuminant on

the reconstruction of NIR spectra using multispectral

imaging methods. We used principal component analysis

(PCA) and a non-linear method (NLE) based on a second

order polynomial in order to obtain reflectance spectra in

the NIR region using CCD camera measurements under

several lighting conditions. The analyzed illuminants were

IS&T's 2003 PICS Conference

540

graybody radiators with color temperatures between 1000

K and 16000 K with the same radiant flux for both

methods and illuminants with color temperature 3371 K

and different radiance values in the case of the NLE

method. In the first part of the study, we used five equi-

spaced Gaussian filters in order to reconstruct the spectral

reflectance of 30 textile samples. We determined the

optimum spectral bandwidth of the filters in order to obtain

the best possible reconstruction for each analyzed case,

that is, for each illuminant and tested method. According to

the results obtained, we analyzed a set of commercially

available interference filters (Thermo Corion) and analyzed

the quality of reconstruction achieved with these filters

under different lighting conditions. The results obtained

show that Prec > 99.9 % and RMSE < 1 in all the analyzed

cases. This indicates that, with the same set of filters, we

can obtain good reconstructions for all the considered

illuminants in the NIR region.

Acknowledgments

This research was supported by the Comisión

Interministerial de Ciencia y Tecnología (CICYT) (Spain)

under grants TAP-99-0856 and DPI2002-00118. M.

Vilaseca would like to thank the Generalitat (Government)

of Catalonia for the PhD grant she has received.

References

1. G. C. Holst, CCD Arrays, Cameras and Displays, SPIE

Press, Bellingham, WA, 1998.

2. G. C. Holst, Solid-state Cameras in Handbook of Optics III,

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Maître, Multispectral Image Acquisition and Simulation of

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Technology, John Wiley & Sons, Chichester, England,

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Camera Measurements, Applied Optics (accepted),

December 2002.

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Biography

Meritxell Vilaseca completed her BSc Degree in Physics

at the Autonomous University of Barcelona in 2000. She

completed her Degree in Optics and Optometry at the

Technical University of Catalonia in 1996. She is currently

enrolled on the PhD program in Optical Engineering at the

Technical University of Catalonia. Her work focuses on

camera calibration and characterization, industrial

colorimetry, color management and imaging.

e-mail: mvilasec@oo.upc.

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Illuminant Influence On The Reconstruction Of NIR Spectra 3371 0deec5231f9b126b3b000000

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