Measurement of normalized spectral responsivity of digital imaging devices by using a LED-based tunable uniform source

doi:10.1364/AO.52.001263

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Measurement of normalized spectral responsivity of digital imaging devices by using a LED-based tunable uniform source

Khaled Mahmoud, Seongchong Park, Seung-Nam Park, and Dong-Hoon Lee »View Author Affiliations

Applied Optics, Vol. 52, Issue 6, pp. 1263-1271 (2013)
http://dx.doi.org/10.1364/AO.52.001263

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– Abstract
Introduction
Instrumentation
Measurement Results
Summary
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Abstract

We present an instrumentation solution for measurement of normalized spectral responsivity of digital imaging sensors and cameras. The instrument consists of multiple light-emitting diodes (LEDs), a single-grating monochromator, and a small-size integrating sphere. Wavelength tuning is achieved by a proper selection of LED in accordance with the monochromator setting in a range from 380 to 900 nm. High spectral purity with a bandwidth of 5 nm is realized without using double gratings and order-sorting filters. Experimental characteristics and calibration of the instrument are described with the related error and uncertainty sources. The performance is demonstrated by measuring a monochrome charge-coupled device and a trichromatic complementary metal–oxide–semiconductor device. The measurement uncertainty is evaluated to be less than 1% ( $k = 2$ ) except several wavelengths with low LED power.

1. Introduction

Digital imaging devices based on charge-coupled device (CCD) or complementary metal–oxide–semiconductor (CMOS) are widely used in a variety of scientific applications [1

G. C. Holst and T. S. Lomheim, CMOS/CCD Sensors and Camera Systems (SPIE, 2007).

]. In radiometry, imaging devices are of great importance for carrying out certain types of measurements that should otherwise be performed by means of scanning devices. They are also the essential elements for multispectral imaging, including color imaging, that becomes a powerful tool in many application fields like biomedical science, remote sensing, arts, and color science.

For scientific applications of digital imaging devices, the technical specifications, such as spatial resolution, quantum efficiency, spectral responsivity, linearity, geometric fidelity, and response time are required to be carefully characterized. In the radiometric and colorimetric applications, measurement of spectral responsivity is of particular importance, which is defined as the ratio of output digital reading to input radiometric quantity as a function of wavelength [2

“Spectral responsivity measurements of detectors, radiometers, and photometers,” International Commission on Illumination (CIE) Publication No. 202 (2011).

]. Since the gain of digital sensors can be easily adjusted and manipulated, the normalized values of spectral responsivity provide the essential information for further characterization and calibration of the radiometric and colorimetric imaging devices [3

H.-C. Lee, Introduction to Color Imaging Science (Cambridge University, 2005).

]. Once the normalized spectral responsivity is measured, absolute calibration of the instrument, i.e., adjustment of the electronic gain and data acquisition algorithm, can be performed at a spectrally integrated calibration source suitable for the target application.

A straightforward way to measure the spectral responsivity of an imaging device is to irradiate it uniformly so that each individual detector receives the same and known amount of optical radiation from a wavelength-tunable monochromatic source. A uniform source can be effectively realized by using an integrating sphere [4

W. A. Hovis and J. S. Knoll, “Characteristics of an internally illuminated calibration sphere,” Appl. Opt. 22, 4004–4007 (1983). [CrossRef]

]. However, the choice of a wavelength-tunable monochromatic source requires a careful consideration. The conventional choice for this is the combination of a white-spectrum (incandescent or discharge) lamp and a monochromator. Such a monochromator-based tunable source can scan a wide wavelength range with adjustable interval and bandwidth, but the spectral power and spectral purity are limited by the performance of the used monochromator [2

“Spectral responsivity measurements of detectors, radiometers, and photometers,” International Commission on Illumination (CIE) Publication No. 202 (2011).

]. In order to achieve a high spectral purity, a double-grating configuration for a low stray level is required which, on the other hand, reduces the spectral output power passing through the monochromator. Recently, tunable laser-based integrating sphere sources are demonstrated at several national metrology institutes as the high-accuracy solution for spectral responsivity measurement of imaging devices [5

A. Ferrero, J. Campos, and A. Pons, “Low-uncertainty absolute radiometric calibration of a CCD,” Metrologia 43, S17–S21 (2006). [CrossRef]

V. E. Anderson, N. P. Fox, and D. H. Nettleton, “Highly stable, monochromatic and tunable optical radiation source and its application to high accuracy spectrophotometry,” Appl. Opt. 31, 536–545 (1992). [CrossRef]

S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, “Facility for spectral irradiance and radiance responsivity calibrations using uniform sources,” Appl. Opt. 45, 8218–8237 (2006). [CrossRef]

–8

M. Schuster, S. Nevas, A. Sperling, and S. Voelker, “Spectral calibration of radiometric detectors using tunable laser sources,” Appl. Opt. 51, 1950–1961 (2012). [CrossRef]

]. However, the coverage of a large wavelength range requires a large and expensive laser facility, which is far from a practical instrumentation for industrial or field applications.

In this paper, we present a new instrumentation scheme for measuring the normalized spectral responsivity of digital imaging devices, which consists of light-emitting diodes (LEDs), a single-grating monochromator, and an integrating sphere [9

K. Mahmoud, S. Park, S.-N. Park, and D.-H. Lee, “LED-based tunable monochromatic uniform source for calibration of imaging sensors and cameras,” in Proceedings of the 11th International Conference on New Developments and Applications in Optical Radiometry (NEWRAD, 2011), pp. 118–119.

,10

K. Mahmoud, S. Park, S.-N. Park, and D.-H. Lee, “Measurement of normalized spectral response of digital imaging sensors using a LED-based tunable uniform source,” in Proceedings of the XX IMEKO World Congress (IMEKO, 2012), paper TC7-O-14.

]. LEDs are compact, cost-effective, efficient, and commercially available at different wavelengths covering from UV through IR. Various tunable quasi-monochromatic sources based on LEDs for radiometric applications are already reported [11

I. Fryc, S. W. Brown, G. P. Eppeldauer, and Y. Ohno, “LED-based spectrally tunable source for radiometric, photometric, and colorimetric applications,” Opt. Eng. 44, 111309 (2005). [CrossRef]

G. Zaid, S.-N. Park, S. Park, and D.-H. Lee, “Differential spectra responsivity measurement of photovoltaic detectors with a LED-based integrating sphere source,” Appl. Opt. 49, 6772–6783 (2010). [CrossRef]

–13

B. H. Hamadani, J. Roller, B. Dougherty, and H. W. Yoon, “Versatile light-emitting-diode-based spectral response measurement system for photovoltaic device characterization,” Appl. Opt. 51, 4469–4476 (2012). [CrossRef]

]. However, the relatively large spectral bandwidth ranging from 20 to 50 nm limits the use of LEDs as a spectral source. To overcome this shortcoming, we use a compact single-grating monochromator as a tunable spectral filter between LEDs and an integrating sphere to develop a uniform source with a spectral bandwidth smaller than 5 nm. By selecting a proper LED in accordance to the wavelength setting of the monochromator, the spectral power could be optimized without reducing the spectral purity.

We show measurement results for two digital imaging device samples, one monochrome (B/W) CCD and one trichromic CMOS, by using the LED-based tunable uniform source. The measurements are performed both in irradiance mode for bare sensors and in radiance mode for cameras. Measurement accuracy is verified by evaluating the measurement uncertainty and systematic error sources for the case of normalized spectral responsivity. The achieved performance shows a high potential of the instrument as a practical solution for industrial applications with a compact and cost-effective setup.

2. Instrumentation

A. Experimental Setup

Figure 1 schematically shows the experimental setup for measuring the normalized spectral response of digital imaging sensors and cameras. The LED-based tunable uniform source consists of LEDs mounted on a rotational disk, a compact single-grating monochromator, and a barium sulfate (

{BaSO}_{4}

) coated integrating sphere with an inner diameter of 50 mm. The LED disk operates the selected one from multiple mounted LEDs at a predefined position [12

]. We used 25 LEDs of different wavelengths to cover the wavelength range from 380 to 900 nm.

Fig. 1. Schematic diagram of the normalized spectral responsivity measurement setup (top view).

The radiation emitted from the selected LED is coupled into the monochromator (Spectral Products, model CM110, focal length 110 mm,

f / 3.9

, slit width 0.6 mm) by using two planoconvex lenses with a diameter of 25.4 mm and a focal length of 20 mm. The spectrally filtered radiation from the monochromator is then coupled into the integrating sphere by using a focusing lens through a sphere port with a diameter of 12.7 mm. A focusing lens is used to form an image of the monochromator output slit with a size of

3 mm \times 10 mm

on the sphere inner wall opposite to the input port so that the light is distributed inside the sphere only after the first diffuse reflection at the sphere wall. No baffle is used inside the sphere as the direct irradiation of the ports by the incident light is effectively avoided though the beam spot control. The choice of the sphere size was the result of a compromise between the irradiance level and the spatial uniformity of the irradiance distribution inside the sphere. The irradiance level inside the integrating sphere is monitored by a Si photodiode attached at another sphere port with a diameter of 12.7 mm. As we calibrate the signal of this photodiode with respect to spectral irradiance at the position of the device under test (DUT), we refer it as the reference detector (REF). The third port of the integrating sphere has a diameter of 25.4 mm and is used as the output port of the tunable uniform source. All three ports are placed so that the normal axes of all the ports are mutually perpendicular (see Fig. 1).

Two different types of DUT can be measured with the LED-based tunable uniform source. A bare imaging sensor, which needs to be calibrated with respect to spectral irradiance at a specific position, is placed in front of the output port at a distance of approximately 10 mm (irradiance mode measurement). Alternatively, an imaging camera including a lens system for calibration with respect to spectral radiance is placed at a distance corresponding to the focal length of the lens system (radiance mode measurement). For the irradiance mode measurement, the DUT sensor is mounted on a computer-controlled three-axis translation stage for a precise and reproducible positioning. The complete setup is mounted on a ground plate with a size of less than

1 m \times 1 m

and controlled with computer software for an automated measurement.

B. Source Characteristics and Measurement Procedure

The basic characteristics of the LED-based tunable uniform source, which can influence the accuracy of the normalized spectral responsivity measurement, are experimentally tested. The measurement procedure is then optimized to avoid or minimize the related error or uncertainty sources.

1. Output Radiant Power

Figure 2(a) shows spectral power distribution of 25 LEDs used for the tunable uniform source, which is measured at the entrance slit of the monochromator by using a spectroradiometer (Instrument System, model CAS140) with a resolution bandwidth of approximately 3 nm. Depending on materials and constructions of LEDs, each LED provides different power level and different spectral bandwidth. Note that we used only the LEDs, which are commercially available (supplied by Roithner Laser Technik, Austria; super bright lamp type, 5 mm diameter round package with clear dome lens, 8° viewing angle).

Fig. 2. (a) Spectral power distribution of the individual LEDs used for the LED-based tunable uniform source. Different colors of the curves correspond to different 25 LEDs, which had been lit one by one during the wavelength scan. (b) Plot of the relative irradiance available at the output port of the integrating sphere source as a function of wavelength measured with an interval of 5 nm (dot symbols). The error bars correspond to repeatability uncertainties of each measurement points.

Selection of LED is correlated with the wavelength setting of the monochromator: as the measurement wavelength is set by an operator, the computer software automatically controls the monochromator, the rotational disk position, and the LED driving circuit to turn on one LED that can provide the maximum radiant power at that wavelength. The output radiant power from the monochromator, therefore, depends not only on the input LED power but also on the coupling and transmission through the grating monochromator at each wavelength. Figure 2(b) shows the relative change of irradiance as the wavelength scans from 380 to 900 nm with an interval of 5 nm. The irradiance at each wavelength is measured by using a calibrated photodiode with an active area of

1 {cm}^{2}

at a distance of 10 mm in front of the sphere output port. The uncertainties shown in Fig. 2(b) as error bars are calculated from repeated scans of the normalized irradiance measurement. We can confirm that the repeatability uncertainty is large at the wavelengths with low irradiance values, which will propagate to the uncertainty of spectral responsivity measurement. The absolute values of irradiance are not accurately known because we could not accurately determine the size of the active area as well as the uniformity of its responsivity. Nevertheless, based on the specification of the photodiode, we could estimate that all the values of the irradiance in Fig. 2(b) lie within a range from 10 to

100 nW / {cm}^{2}

. Considering the geometric condition, this range of irradiance corresponds to a range of radiance from 5 to

50 nW / {cm}^{2} sr

. We note that we have intentionally reduced the coupling efficiency of LED at several set wavelengths, at which the intrinsic output LED power is extremely high compared to other LEDs, in order to minimize error due to nonlinearity of signal readings.

2. Spectral Purity

The spectral characteristics of output radiant power at each wavelength are checked by using the scanning-type spectroradiometer (Instrument System, model Spectro 320) with a resolution bandwidth of 0.25 nm. The spectral bandwidth is measured to be less than 5 nm as a full width at half-maximum for the whole tuning range from 380 to 900 nm. The measured spectral bandwidth was in accordance with the specification of the used single-grating monochromator with a

f

-number of 3.9 and a slit width of 0.6 mm.

In addition, the spectral stray light is measured by scanning the spectroradiometer with a large resolution bandwidth of 5 nm in the range far from the set wavelength of the monochromator. Up to the dynamic range limit of

10^{4}

, no out-of-band stray light could be identified. This high spectral purity with low stray light is one of the important advantage of the colored LED-monochromator system in comparison with the conventional white lamp-mochromator system [2

“Spectral responsivity measurements of detectors, radiometers, and photometers,” International Commission on Illumination (CIE) Publication No. 202 (2011).

]. Since the LEDs are intrinsically quasi-monochromatic with emission bandwidth of less than 50 nm, no output of higher-order diffraction is expected. Therefore, no order-sorting filter is required, which is indispensable for the lamp system to cover a wide wavelength tuning range. Moreover, the ratio between the in-band power and the out-of-band power for the LED system is much less than the case for the lamp system, which results in a reduced stray light level. As a consequence, the LED-monochromator system could be realized based on a simple high-throughput, single-grating monochromator without concern about the spectral purity.

3. Temporal Power Stability

The measurement of normalized spectral responsivity is based on a comparison between the REF signal and the DUT signal at the same radiation provided by the tunable uniform source. Temporal instability of radiant power during the both signal readings, therefore, causes an error in their ratio measurement. In order to achieve a stable radiant power, each LED selected for a specific wavelength is operated with a constant forward current by using a precision source meter. However, we noticed that each LED shows a characteristic power drift within a duration of several minutes after turning on, which is probably due to a thermalization in the LED [9

,10

]. Since the emission characteristics of LEDs is sensitive to temperature at the p–n junction, such a power drift is not to be avoided for the setup where the junction temperature of the LEDs is not actively stabilized [14

S. Park, Y.-W. Kim, D.-H. Lee, and S.-N. Park, “Preparation of a standard light-emitting diode (LED) for photometric measurements by functional seasoning,” Metrologia 43, 299–305 (2006). [CrossRef]

In order to minimize the error due to the temporal power instability, we built a drift check algorithm in the measurement software. At each set value of wavelength, the readings of the REF and DUT signals is repeated twice in the sequence

REF (t_{1}) \to DUT (t_{2}) \to REF (t_{3})

, where

REF (t)

and

DUT (t)

denote the recordings of the REF and DUT signals at a time of

t

, respectively. The recording of the REF corresponds to a reading of the averaged REF photocurrent by a calibrated ammeter, while the recording of the DUT corresponds to capturing of its digital image data as a single shot. The software compares then the relative difference of the REF readings at

t_{1}

and

t_{3}

, which corresponds to the relative power drift during the signal recordings for the ratio measurement. The software repeats the measurement sequence at this wavelength until the relative power drift between

REF (t_{1})

and

REF (t_{3})

is less than a predefined criterion of 0.1%. This has a consequence that the measurement software waits until the LED lit for that wavelength reaches a sufficient power stability. The measurement error due to a power drift is limited to be smaller than 0.1% for the whole wavelength range. We note that the short-term power instability is additionally considered as a repeatability uncertainty of the readings of the averaged REF photocurrent both at

t_{1}

and

t_{3}

with a number of sampling of more than 10 for each reading.

4. Spatial Uniformity

For an integrating sphere with a finite port size, the spectral irradiance at the output port is not perfectly uniform, but shows a distribution which varies smoothly across the port [4

W. A. Hovis and J. S. Knoll, “Characteristics of an internally illuminated calibration sphere,” Appl. Opt. 22, 4004–4007 (1983). [CrossRef]

]. If two detectors are to be compared at such a nonuniform irradiance field, the difference in detector size or position causes a systematic error [12

]. Therefore, characterization of spatial uniformity of the irradiance distribution at the position of DUT provides useful information for error and uncertainty analysis.

Figure 3(a) shows the spatial irradiance distribution of the LED-based tunable uniform source, which is measured at a distance of 10 mm from the output port through a horizontal scan at different wavelengths from 400 to 800 nm. For this measurement, a monochrome CCD sensor is used as a DUT mounted on the computer-controlled translation stage. While the CCD sensor is moved on the horizontal axis crossing the output port through the center (

x

-axis in Fig. 1), the digital images are captured at different positions. The raw data at each position was the averaged value of the pixels in a fixed area of interest (AOI) with a size of

20 \times 20

pixels corresponding to approximately

0.1 mm \times 0.1 mm

. The measured raw data are then normalized to the value at the center position of the output port. Such a measurement of the normalized irradiance distribution is repeated at different wavelengths. We verify in Fig. 3(a) that the spatial uniformity of irradiance is limited only in a small area at the center of the output port. Such a nonuniform distribution can cause a significant error when the absolute irradiance responsivity should be measured by comparing two detectors with different sizes [12

Fig. 3. (a) Spatial irradiance distribution of the LED-based tunable uniform source measured at a distance of 10 mm from the output port through a horizontal scan in 1 mm steps at different wavelengths (dot symbols). The connecting curves are only for better visibility. (b) Plot of the relative difference of the spatial irradiance distribution with respect to the average values of the different wavelengths within a range of

\pm 15 mm

at the center of the output port.

However, concerning only measurement of the normalized values of the spectral irradiance responsivity, the nonuniformity of irradiance distribution itself does not affect the accuracy, as long as the positioning of the DUT is reproducible. Instead, the major concern is the spectral dependence of the spatial irradiance distribution. From Fig. 3(a), we confirm that the spatial irradiance distribution measured at different wavelengths show a good overlap. In order to verify it more precisely, we plotted in Fig. 3(b) the relative difference of the spatial irradiance distribution with respect to the average values of the different wavelengths, which are calculated from the data of Fig. 3(a) within a range of

\pm 15 mm

at the center of the output port. We confirm that the wavelength dependence of irradiance distribution is smaller than

\pm 0.5 %

in the range of

\pm 5 mm

near the center, which is comparable to the uncertainty of the signal readings (see Table 2 and Fig. 5). Outside the central range, the random scattering of the data increases, as expected, from the decreased level of the DUT signal. No significant wavelength dependence of spatial irradiance distribution could be identified within the limit of the measurement uncertainty. From the spatial uniformity measurements in Fig. 3, we conclude that the error due to spatial nonuniformity of irradiance can be minimized for the normalized spectral responsivity measurement by positioning a calibration detector or a test detector with high precision and reproducibility. In our setup of Fig. 1, we used the translation stage which can control the absolute position within

\pm 0.01 mm

(Sigma Koki, SGSP model series).

5. Stray Light

The REF detector attached to the integrating sphere monitors the radiant power level delivered from the LED-based tunable source into the sphere, and will be calibrated against the spectral irradiance at a fixed point in front of the output port (see Fig. 1). Any ambient stray light which enters through the output port will change the REF reading and cause a measurement error. In general, the ambient stray can be easily corrected by a dark signal reading with a shutter inside the monochromator. We performed the dark signal readings of both REF and DUT prior to the main measurement procedure and subtracted them from the final signal readings. The complete setup is placed inside a light-tight box to keep the ambient stray as low as possible.

The specific problem related to our instrumentation is the stray due to reflection from the DUT when it is placed close to the output port for the irradiance mode measurement. In this condition, the light from the output port is reflected from the detector surface and chassis of the test sensor and comes back into the integrating sphere as an additional stray. Since this stray exists only in the presence of the radiant power input, it cannot be corrected by the dark readings. We have experimentally tested the amount of the reflection stray by using different chassis materials at the position of DUT. We compared a chassis of bare black-anodized Aluminum and a chassis coated with a low-reflectance paint (3M/Mankiewicz, NEXTEL Velvet 811-21) at a distance of below 20 mm from the output port. As a result, we confirmed a significant change of the REF readings depending on the chassis materials. Especially for wavelengths above 700 nm, where the reflectance of black-anodized aluminum increases, the difference between two chassis materials were as large as 10% in the REF signal.

In order to eliminate such an error due to the stray by reflection, we designed the measurement procedure so that the DUT in the irradiance mode is moved to a predefined “zero” position outside the output port, whenever the REF reading is performed. For the DUT reading, the DUT is moved back to the test position in front of the output port. This procedure is easily realized with the computer-controlled translation stage mounting the DUT in the irradiance measurement mode. We note that such a DUT movement is not required for the radiance mode measurement with a DUT at a large distance (

> 100 mm

) from the output port, because the change of the REF reading due to reflection from the DUT was negligible.

C. Instrument Calibration

Calibration of the instrument is performed in two steps. First, the wavelength scale of the monochromator is calibrated. Two pencil-type calibration lamps of Hg(Ar) and Ar are placed at the input slit of the monochromator and the transmitted light is recorded at the output slit by using a photodiode while scanning the wavelength with a small step of 0.2 nm. The instrument values of the peak wavelengths of selected isolated emission lines are compared with the literature values. The maximum difference of the instrument wavelength from the literature value was 0.73 nm in a range from 380 to 900 nm. From this measurement, we declared that the wavelength scale of the tunable source is calibrated with a standard uncertainty of wavelength

u (λ) = 0.42 nm

, which is estimated from

0.73 nm / \sqrt 3

by assuming a rectangular probability distribution [15

Evaluation of measurement data—guide to the expression of uncertainty in measurement (JCGM, 2008).

Second, the responsivity of the REF photocurrent reading (in A) is calibrated against the irradiance (in

{W m}^{- 2}

) at the position of the DUT close to the output port as a function of wavelength. However, as our aim is to measure the normalized spectral responsivity of the DUT, the absolute values of the REF responsivity (in

{A W}^{- 1} m^{2}

) is not of interest. Instead, we use only the normalized values of the REF responsivity.

For calibration of the REF responsivity, a single-element Si photodiode (Hamamatsu S1337-1010BQ, active area

10 mm \times 10 mm

) with the known spectral responsivity is mounted as a standard detector (STD) at the place of DUT in the irradiance mode. The spectral power responsivity of the STD, which we denote as

S_{STD} (λ)

, is calibrated against the KRISS spectral responsivity scale from 300 to 1000 nm with relative standard uncertainties from 0.2% to 0.4% (

k = 1

) depending on wavelength [16

R. Goebel and M. Stock, “Report on the comparison CCPR-K2.b of spectral responsivity measurements in the range 300 nm to 1000 nm,” Metrologia 41, 02004 (2004). [CrossRef]

]. The calibration equation for the REF responsivity

S_{REF} (λ)

is then given by

S_{REF} (λ) = \frac{y_{REF}}{y_{STD}} \cdot S_{STD} (λ),

(1)

where

y_{REF}

and

y_{STD}

denote the readings of the REF and of the STD, respectively. Note that the reading of detectors used in this paper always corresponds to the dark-subtracted signal. For the measurement of the normalized spectral responsivity of an imaging sensor or camera, we use only the relative values of the REF spectral responsivity

S_{REF}^{*} (λ)

which are normalized, e.g., to its maximum value:

S_{REF}^{*} (λ) = \frac{S_{REF} (λ)}{S_{REF}^{\max}} .

(2)

Figure 4 shows the experimental calibration result of the instrument which is a plot of the normalized REF responsivity

S_{REF}^{*} (λ)

as a function of wavelength measured from 380 to 900 nm with a step of 5 nm. The calibration measurements are repeated and averaged at different distances of the STD to the output port from 10 to 25 mm with a step of 5 mm. The distance dependence of the normalized REF responsivity is included as a random uncertainty component into the uncertainty budget. The error bars in Fig. 4 indicate the combined expanded uncertainty with a coverage factor

k = 2

for a confidence level of approximately 95% [15

Evaluation of measurement data—guide to the expression of uncertainty in measurement (JCGM, 2008).

]. The uncertainty depends on wavelength mainly because the radiant power of the LED-based tunable source strongly varies with wavelength as shown in Fig. 2(b). In addition, the uncertainty of the STD responsivity is also wavelength dependent.

Fig. 4. Spectral responsivity of the REF as measured against the standard photodiode mounted at a close distance to the output port. The error bars represent the associated uncertainties of this calibration.

The uncertainty budget for the REF spectral responsivity

S_{REF} (λ)

according to Eq. (1) is shown in Table 1, as an example, at 435 nm, where the combined uncertainty was the lowest. Expressed as relative uncertainties, the budget is valid also for the normalized values in Eq. (2). The uncertainty component of type A and B correspond to the component evaluated with a statistical method and with a nonstatistical method, respectively [15

Evaluation of measurement data—guide to the expression of uncertainty in measurement (JCGM, 2008).

]. For the type A components, the number of repetition is also indicated in the parentheses.

Table 1. Uncertainty Budget of the REF Responsivity Calibration at 435 nm

Related Quantity in Eq. (1)	Uncertainty Component Description	Evaluation Type	Probability Distribution	Relative Standard Uncertainty
$y_{REF}$	Repeatability of the REF reading	A (50)	t	0.03%
	Nonlinearity of current measurement device	B	Rectangular	0.05%
$y_{STD}$	Repeatability of the STD reading	A (50)	t	0.02%
	Nonlinearity of current measurement device	B	Rectangular	0.3%
$y_{REF} / y_{STD}$	Wavelength calibration of monochromator	B	Rectangular	0.01%
	Distance dependence of calibration	A (5)	t	0.22%
	Radiant power drift	B	Rectangular	$< 0.1 %$
$S_{STD} (λ)$	Calibration uncertainty of the STD responsivity	B	Normal	0.25%
$S_{REF} (λ)$	Combined standard uncertainty of the REF responsivity		Normal	0.46%

All the uncertainty components in Table 1 can be evaluated directly from the data of each quantity in Eq. (1) except the uncertainty of the signal ratio with respect to the wavelength calibration uncertainty. The propagation of the wavelength uncertainty

u (λ)

to the uncertainty of a ratio measurement is described in [17

S. Park, D.-H. Lee, Y.-W. Kim, and S.-N. Park, “Uncertainty evaluation for the spectroradiometric measurement of the averaged light-emitting diode intensity,” Appl. Opt. 46, 2851–2858 (2007). [CrossRef]

]. From Eq. (1), we derive the relation between the relative uncertainty of the ratio

y_{REF} / y_{STD}

and the absolute uncertainty of wavelength

u (λ)

u_{rel} (\frac{y_{REF}}{y_{STD}}) = (\frac{1}{y_{REF}} \cdot \frac{\partial y_{REF}}{\partial λ} - \frac{1}{y_{STD}} \cdot \frac{\partial y_{STD}}{\partial λ}) \cdot u (λ) .

(3)

Note that the uncertainty of a ratio of two quantities due to an inaccurate setting of wavelength depends on the difference of the spectral slopes of both the quantities.

D. Data Acquisition of Imaging Device

Once the instrument is calibrated, the standard photodiode is removed and an imaging device as a DUT is mounted for measurement. If the DUT is a bare digital image sensor without a lens system, it is measured in the irradiance mode at a distance of approximately 10 mm to the output port. If the DUT is a digital camera with an imaging optics, the measurement is performed in the radiance mode at a distance of the focal length of the imaging lens system (see Fig. 1). The imaging device is connected with the computer via an USB interface for control and data communication.

In the measurement procedure of normalized spectral responsivity of the DUT, one DUT reading at each wavelength corresponds to a capture of its digital image data as a single shot. All the DUT readings during the wavelength scan of the whole measurement range should be performed at a fixed gain and exposure of the DUT, which are to be set for an optimal signal-to-noise ratio prior to the scan measurement. The collected batch of digital images for one wavelength scan is then treated by a separate data acquisition program, which calculates the average and the standard deviation of pixel values within a predefined AOI for each image. Normally, we set

20 \times 20

pixels at the center of the image as AOI. The average value of the pixel data in the AOI is denoted as the reading of the DUT at a wavelength of

λ

y_{DUT} (λ)

, and the measurement equation of the normalized spectral responsivity of the DUT,

S_{DUT} (λ)

, is now given by

S_{DUT} (λ) = \frac{y_{DUT}}{y_{REF}} \cdot S_{REF}^{*} (λ) .

(4)

If necessary, the final result can be renormalized to its maximum value or to any value at a specific normalization wavelength

λ_{norm}

S_{DUT}^{*} (λ) = \frac{S_{DUT} (λ)}{S_{DUT} (λ_{norm})} .

(5)

3. Measurement Results

A. Monochrome CCD Sensor and Camera

The first DUT we have measured was a monochrome (B/W) progressive scan CCD sensor (Sony, model ICX205AL,

1280 \times 1024

pixels, pixel size

4.65 μm \times 4.65 μm

), which is integrated into a digital camera device with an 8 bit analog-to-digital (A/D) converter (ThorLabs, model DCU 224M).

Figure 5 shows the measured normalized spectral responsivity of the CCD sensor with expanded uncertainty as error bars (

k = 2

). We see the increased uncertainties at several wavelengths due to weak radiant power of the LED-based tunable source. As the average digital counts at these wavelengths are low, the uncertainty of resolution becomes significant, which also causes abrupt changes of the spectral data. Nevertheless, most of the measurement data in the range from 380 to 900 nm have the relative expanded uncertainties of less than 1% (

k = 2

). The lowest uncertainty is achieved again at the points, where the average count of the DUT was the highest.

Fig. 5. Normalized spectral responsivity of a monochrome CCD sensor measured in the irradiance mode. The error bars represent the associated uncertainties of this measurement.

The uncertainty budget of the measurement result of the monochrome CCD sensor in Fig. 5 is representatively presented in Table 2 for the wavelength of 435 nm. The most significant component beside the calibration uncertainty is the resolution uncertainty of the DUT reading. As the resolution of the digital data is fixed to be unity, the resolution uncertainty depends on the average count of the pixel data in the AOI. For

y_{DUT} = 244

at 435 nm, we calculate the relative uncertainty due to resolution by

(1 / 244) / 2 \sqrt 3 = 0.12 %

by assuming a rectangular probability distribution. Compared to Table 1, several systematic components are absent in Table 2 because these components are once considered in the uncertainty of the REF responsivity. For Table 2, the equation for the uncertainty due to wavelength inaccuracy in Eq. (3) should be modified in accordance with Eq. (4) to

u_{rel} (\frac{y_{DUT}}{y_{REF}}) = (\frac{1}{y_{DUT}} \cdot \frac{\partial y_{DUT}}{\partial λ} - \frac{1}{y_{REF}} \cdot \frac{\partial y_{REF}}{\partial λ}) \cdot u (λ) .

(6)

Table 2. Uncertainty Budget of the Normalized Spectral Responsivity Measurement for a Monochrome CCD Sensor at 435 nm

Related Quantity in Eq. (4)	Uncertainty Component Description	Evaluation Type	Probability Distribution	Relative Standard Uncertainty
$y_{DUT}$	Repeatability of the DUT reading	A (400)	t	0.10%
	Resolution	B	Rectangular	0.12%
$y_{REF}$	Repeatability of the REF reading	A (50)	t	0.03%
	Nonlinearity of current measurement device	B	Rectangular	0.05%
$y_{DUT} / y_{REF}$	Wavelength calibration of monochromator	B	Rectangular	0.01%
	Radiant power drift	B	Rectangular	$< 0.1 %$
$S_{REF}^{*} (λ)$	Calibration uncertainty of the REF responsivity (see Table 1)	B	Normal	0.46%
$S_{DUT} (λ)$	Combined standard uncertainty of the REF responsivity		Normal	0.49%

The radiance mode measurement is demonstrated for an imaging camera, in which the same monochrome CCD sensor is used. A camera lens system (AVENIR zoom lens, back focal length 50 mm,

f / 1.3

) is attached to the CCD sensor, and the camera is placed at a distance of approximately 500 mm. The focal length of the lens system is adjusted so that we see a well-focused image of the output port. The camera is aligned so that the AOI is placed at the center of the output port while the size of the AOI is kept much smaller than that of the output port image.

Figure 6 shows the measured normalized spectral responsivity of the CCD camera as dot symbols. The error bars indicate the expanded uncertainty of the measurement (

k = 2

). The dashed curve corresponds to the CCD sensor result of Fig. 5, which is plotted together for comparison. The measurement uncertainty of the camera is not very different from that of the sensor. However, we can clearly recognize the effect of the lens system to the spectral responsivity from comparison of the two results. Especially in the short wavelength range, the transmission of the used lens system seems to be low so that the responsivity of the camera tends to nearly zero. These measurement results demonstrate the practicability of our instrument, which can measure both imaging sensors and cameras without extra calibration.

Fig. 6. Normalized spectral responsivity of a monochrome CCD camera measured in the radiance mode (dot symbols). The error bars represent the associated uncertainties of this measurement. The dashed curve is the result of the CCD sensor in the camera, which is measured in the irradiance mode and shown in Fig. 5.

B. Trichromatic CMOS Sensor and Camera

As the second DUT, we measured a trichromatic CMOS-based device with an 8 bit A/D converter (HVS, model HVR-2300CA,

2048 \times 1536

pixels, pixel size

3.2 μm \times 3.2 μm

). The measurement procedure was the same as the case with the CCD device. However, the data acquisition is modified because three different values of red (R), green (G), and blue (B) channels are assigned to each pixel. We treated three channels as independent devices. However, the normalization of three channels is done to the same wavelength of 550 nm in order to compare their responsivities to each other.

Figure 7 shows the measured normalized spectral responsivity of the trichromatic CMOS sensor in the irradiance mode with expanded uncertainty as error bars (

k = 2

). The spectral shapes and overlaps of the three channels can be clearly recognized. The responsivity above 680 nm is close to zero because the CMOS sensor contains an infrared-cutting filter in front of the sensor.

Fig. 7. Normalized spectral responsivity of a trichromatic CMOS sensor measured in the irradiance mode. The error bars represent the associated uncertainties of this measurement.

Figure 8 shows the result of the CMOS camera. For this measurement, the camera lens system used for the monochromatic CCD sensor is attached to the CMOS sensor. For comparison, the results of the CMOS sensor of Fig. 7 are plotted together as dashed curves. We see a significant and complex change of the spectral responsivity for the case of the CMOS camera through attaching the lens system. We presume that a multireflection interference between the lens system and the infrared-cutting filter can cause such a change. Figure 8 shows that such influences from lens systems or other optical components to the spectral responsivity of the device can be effectively identified and investigated by using our instrument.

Fig. 8. Normalized spectral responsivity of a tri-chromatic CMOS camera measured in the radiance mode (dot symbols). The error bars represent the associated uncertainties of this measurement. The dashed curve is the result of the CMOS sensor in the camera, which is measured in the irradiance mode and shown in Fig. 7.

4. Summary

We realized a new instrumentation scheme for measurement of normalized spectral responsivity of imaging sensors and cameras, which is based on a LED-based tunable spectral source with an integrating sphere. A combination of 25 LEDs with different colors and a single-grating monochromator provided tunable radiation with a bandwidth of less than 5 nm in a range from 380 to 900 nm. A high spectral purity could be achieved without using order-sorting filters and double-grating configuration.

We experimentally tested the characteristics of the LED-based tunable uniform source, which can affect the accuracy of the measurement. The measurement procedure is then designed and modified to minimize the error and uncertainty sources. The calibration of the instrument is performed by using spectral lamps and a standard photodiode for spectral responsivity.

The instrument is applied to a monochrome CCD device and a trichrome CMOS device. The normalized spectral responsivity is measured both in the irradiance mode for the bare sensors and in the radiance mode for the cameras. The measurement uncertainty is evaluated to be less than 1% except several wavelengths where the radiant power was too low.

In conclusion, we demonstrated a high potential of the LED-based tunable uniform source for practical metrology applications. Replacement of conventional light source by LEDs provides a possibility to realize a cost-effective and compact setup of a monochromatic source. For instance, the intrinsically low spectral stray of the LED-based source makes the double-monochromator configuration and the order-sorting filters unnecessary. Although LEDs cannot provide sufficient radiant power at several wavelengths, careful uncertainty evaluation of the spectral measurement provides sufficient information to identify and bridge these points. Further improvements of the LED-based source are expected by using, e.g., its excellent modulation property.

Acknowledgments

This work was supported by the Korea Research Institute of Standards and Science (KRISS) under the project “Establishment of National Physical Measurement Standards and Improvements of Calibration/Measurement Capability,” grant 12011002.

References

1.	G. C. Holst and T. S. Lomheim, CMOS/CCD Sensors and Camera Systems (SPIE, 2007).
2.	“Spectral responsivity measurements of detectors, radiometers, and photometers,” International Commission on Illumination (CIE) Publication No. 202 (2011).
3.	H.-C. Lee, Introduction to Color Imaging Science (Cambridge University, 2005).
4.	W. A. Hovis and J. S. Knoll, “Characteristics of an internally illuminated calibration sphere,” Appl. Opt. 22, 4004–4007 (1983). [CrossRef]
5.	A. Ferrero, J. Campos, and A. Pons, “Low-uncertainty absolute radiometric calibration of a CCD,” Metrologia 43, S17–S21 (2006). [CrossRef]
6.	V. E. Anderson, N. P. Fox, and D. H. Nettleton, “Highly stable, monochromatic and tunable optical radiation source and its application to high accuracy spectrophotometry,” Appl. Opt. 31, 536–545 (1992). [CrossRef]
7.	S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, “Facility for spectral irradiance and radiance responsivity calibrations using uniform sources,” Appl. Opt. 45, 8218–8237 (2006). [CrossRef]
8.	M. Schuster, S. Nevas, A. Sperling, and S. Voelker, “Spectral calibration of radiometric detectors using tunable laser sources,” Appl. Opt. 51, 1950–1961 (2012). [CrossRef]
9.	K. Mahmoud, S. Park, S.-N. Park, and D.-H. Lee, “LED-based tunable monochromatic uniform source for calibration of imaging sensors and cameras,” in Proceedings of the 11th International Conference on New Developments and Applications in Optical Radiometry (NEWRAD, 2011), pp. 118–119.
10.	K. Mahmoud, S. Park, S.-N. Park, and D.-H. Lee, “Measurement of normalized spectral response of digital imaging sensors using a LED-based tunable uniform source,” in Proceedings of the XX IMEKO World Congress (IMEKO, 2012), paper TC7-O-14.
11.	I. Fryc, S. W. Brown, G. P. Eppeldauer, and Y. Ohno, “LED-based spectrally tunable source for radiometric, photometric, and colorimetric applications,” Opt. Eng. 44, 111309 (2005). [CrossRef]
12.	G. Zaid, S.-N. Park, S. Park, and D.-H. Lee, “Differential spectra responsivity measurement of photovoltaic detectors with a LED-based integrating sphere source,” Appl. Opt. 49, 6772–6783 (2010). [CrossRef]
13.	B. H. Hamadani, J. Roller, B. Dougherty, and H. W. Yoon, “Versatile light-emitting-diode-based spectral response measurement system for photovoltaic device characterization,” Appl. Opt. 51, 4469–4476 (2012). [CrossRef]
14.	S. Park, Y.-W. Kim, D.-H. Lee, and S.-N. Park, “Preparation of a standard light-emitting diode (LED) for photometric measurements by functional seasoning,” Metrologia 43, 299–305 (2006). [CrossRef]
15.	Evaluation of measurement data—guide to the expression of uncertainty in measurement (JCGM, 2008).
16.	R. Goebel and M. Stock, “Report on the comparison CCPR-K2.b of spectral responsivity measurements in the range 300 nm to 1000 nm,” Metrologia 41, 02004 (2004). [CrossRef]
17.	S. Park, D.-H. Lee, Y.-W. Kim, and S.-N. Park, “Uncertainty evaluation for the spectroradiometric measurement of the averaged light-emitting diode intensity,” Appl. Opt. 46, 2851–2858 (2007). [CrossRef]

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3940) Instrumentation, measurement, and metrology : Metrology

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: October 31, 2012
Revised Manuscript: January 10, 2013
Manuscript Accepted: January 11, 2013
Published: February 15, 2013

Citation
Khaled Mahmoud, Seongchong Park, Seung-Nam Park, and Dong-Hoon Lee, "Measurement of normalized spectral responsivity of digital imaging devices by using a LED-based tunable uniform source," Appl. Opt. 52, 1263-1271 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-6-1263

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References

G. C. Holst and T. S. Lomheim, CMOS/CCD Sensors and Camera Systems (SPIE, 2007).
“Spectral responsivity measurements of detectors, radiometers, and photometers,” International Commission on Illumination (CIE) Publication No. 202 (2011).
H.-C. Lee, Introduction to Color Imaging Science (Cambridge University, 2005).
W. A. Hovis and J. S. Knoll, “Characteristics of an internally illuminated calibration sphere,” Appl. Opt. 22, 4004–4007 (1983). [CrossRef]
A. Ferrero, J. Campos, and A. Pons, “Low-uncertainty absolute radiometric calibration of a CCD,” Metrologia 43, S17–S21 (2006). [CrossRef]
V. E. Anderson, N. P. Fox, and D. H. Nettleton, “Highly stable, monochromatic and tunable optical radiation source and its application to high accuracy spectrophotometry,” Appl. Opt. 31, 536–545 (1992). [CrossRef]
S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, “Facility for spectral irradiance and radiance responsivity calibrations using uniform sources,” Appl. Opt. 45, 8218–8237 (2006). [CrossRef]
M. Schuster, S. Nevas, A. Sperling, and S. Voelker, “Spectral calibration of radiometric detectors using tunable laser sources,” Appl. Opt. 51, 1950–1961 (2012). [CrossRef]
K. Mahmoud, S. Park, S.-N. Park, and D.-H. Lee, “LED-based tunable monochromatic uniform source for calibration of imaging sensors and cameras,” in Proceedings of the 11th International Conference on New Developments and Applications in Optical Radiometry (NEWRAD, 2011), pp. 118–119.
K. Mahmoud, S. Park, S.-N. Park, and D.-H. Lee, “Measurement of normalized spectral response of digital imaging sensors using a LED-based tunable uniform source,” in Proceedings of the XX IMEKO World Congress (IMEKO, 2012), paper TC7-O-14.
I. Fryc, S. W. Brown, G. P. Eppeldauer, and Y. Ohno, “LED-based spectrally tunable source for radiometric, photometric, and colorimetric applications,” Opt. Eng. 44, 111309 (2005). [CrossRef]
G. Zaid, S.-N. Park, S. Park, and D.-H. Lee, “Differential spectra responsivity measurement of photovoltaic detectors with a LED-based integrating sphere source,” Appl. Opt. 49, 6772–6783 (2010). [CrossRef]
B. H. Hamadani, J. Roller, B. Dougherty, and H. W. Yoon, “Versatile light-emitting-diode-based spectral response measurement system for photovoltaic device characterization,” Appl. Opt. 51, 4469–4476 (2012). [CrossRef]
S. Park, Y.-W. Kim, D.-H. Lee, and S.-N. Park, “Preparation of a standard light-emitting diode (LED) for photometric measurements by functional seasoning,” Metrologia 43, 299–305 (2006). [CrossRef]
Evaluation of measurement data—guide to the expression of uncertainty in measurement (JCGM, 2008).
R. Goebel and M. Stock, “Report on the comparison CCPR-K2.b of spectral responsivity measurements in the range 300 nm to 1000 nm,” Metrologia 41, 02004 (2004). [CrossRef]
S. Park, D.-H. Lee, Y.-W. Kim, and S.-N. Park, “Uncertainty evaluation for the spectroradiometric measurement of the averaged light-emitting diode intensity,” Appl. Opt. 46, 2851–2858 (2007). [CrossRef]

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